{"id":1114,"date":"2023-07-21T22:16:17","date_gmt":"2023-07-21T22:16:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/?post_type=chapter&#038;p=1114"},"modified":"2023-08-02T05:31:24","modified_gmt":"2023-08-02T05:31:24","slug":"how-to-use-ti-84-plus-ce-or-any-ti-84-family","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/how-to-use-ti-84-plus-ce-or-any-ti-84-family\/","title":{"raw":"How to Use TI-84 Plus CE (or any TI-84 family)","rendered":"How to Use TI-84 Plus CE (or any TI-84 family)"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Graphing a Function on TI-84 Plus CE<\/li>\r\n \t<li>Finding a Minimum\/Maximum Value on TI-84 Plus CE<\/li>\r\n \t<li>Finding Zeros on TI-84 Plus CE<\/li>\r\n \t<li>Solving Polynomial Equations and Inequalities on TI-84 Plus CE<\/li>\r\n \t<li>Using Matrices to Solve Linear System on TI-84 Plus CE<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Graphing a Function on TI-84 Plus CE<\/h2>\r\n<img class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" \/>\u00a0First, to type in a function, press the \"y=\" button.\r\n<ul>\r\n \t<li>Type in the given function as is. If the function is a rational function, please don\u2019t forget to put parentheses around its numerator and denominator or use the fraction form.<\/li>\r\n \t<li><img class=\"size-full wp-image-1120 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_X-T-Theta-n.png\" alt=\"TI-84 Key: X, T, theta, n\" width=\"67\" height=\"51\" \/>\u00a0To type [latex]x[\/latex], use \"X, T, [latex]\\theta[\/latex], n\" button.<\/li>\r\n<\/ul>\r\n<img class=\"size-full wp-image-1123 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Window.png\" alt=\"TI-84 Key: Window\" width=\"69\" height=\"51\" \/>\u00a0Second, to change the view of the function, press the \"Window\" button.\r\n<ul>\r\n \t<li><span style=\"font-size: 1em;\">If the window is given, please change the window: [Xmin, Xmax, Xscl] X [Ymin, Ymax, Yscl]\u00a0<\/span><\/li>\r\n \t<li>Default window is [-10, 10, 1] X [-10, 10, 1]<\/li>\r\n<\/ul>\r\n<img class=\"size-full wp-image-1118 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" \/>\u00a0Third, to see the graph of the function, press the \"Graph\" button.\r\n\r\n<img class=\"size-full wp-image-1122 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Zoom.png\" alt=\"TI-84 Key: Zoom\" width=\"67\" height=\"51\" \/>\u00a0Lastly, if you want to go back to the default window setting, press the \"Zoom\" button. Then choose \"#6: ZStandard\"\r\n<h2>Finding a Minimum\/Maximum Value on TI-84 Plus CE<\/h2>\r\n<img class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" \/><img class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" \/>\u00a0First, graph the function on TI=-84 using the \"y=\" button and the \"graph\" button.\r\n\r\n<img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1117 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png\" alt=\"TI-84 Key: Calc\" width=\"70\" height=\"79\" \/>\u00a0Second, to find the minimum or maximum (or vertex or turning point) of the function, press the \"2nd\" button and the \"trace\" button in order, which is the \"calc\" button. Then choose <strong>\"<span style=\"font-size: 1em;\">#3: minimum or #4: maximum.\"<\/span><\/strong>\r\n<ul>\r\n \t<li><span style=\"font-size: 1em;\">Left Bound [latex]\\rightarrow[\/latex] click on the left side of the minimum\/maximum point<\/span><\/li>\r\n \t<li>Right Bound [latex]\\rightarrow[\/latex] click on the right side of the minimum\/maximum point<\/li>\r\n \t<li>Guess [latex]\\rightarrow[\/latex] optional; don\u2019t need to guess ^^<\/li>\r\n<\/ul>\r\n<div class=\"textbox\">\r\n\r\nSomehow TI often shows some strange decimals. In that case, please round the number and check if it is working for the function.\r\n\r\nFor example, given [latex]f(x)=x^2+2x-6[\/latex],\u00a0TI shows minimum [latex]x=-.9999994, y=-7[\/latex].\r\nSo, the vertex (or minimum) is [latex](-1, -7)[\/latex].\r\nTo check, plug in.\u00a0[latex]f(-1)=(-1)^2+2(-1)-6=1-2-6=-7[\/latex] [It works!]\r\n\r\n<\/div>\r\n<h2>Finding Zeros on TI-84 Plus CE<\/h2>\r\n<img class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" \/><img class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" \/>\u00a0First, graph the function on TI=-84 using the \"y=\" button and the \"graph\" button.\r\n\r\n<img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1117 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png\" alt=\"TI-84 Key: Calc\" width=\"70\" height=\"79\" \/>\u00a0Second, to find the real zero (or [latex]x[\/latex]-intercept) of the function, press the \"2nd\" button and the \"trace\" button in order, which is the \"calc\" button. Then choose <strong>\"<span style=\"font-size: 1em;\">#2: zero.\"<\/span><\/strong>\r\n<ul>\r\n \t<li><span style=\"font-size: 1em;\">Left Bound [latex]\\rightarrow[\/latex] click on the left side of the minimum\/maximum point<\/span><\/li>\r\n \t<li>Right Bound [latex]\\rightarrow[\/latex] click on the right side of the minimum\/maximum point<\/li>\r\n \t<li>Guess [latex]\\rightarrow[\/latex] optional; don\u2019t need to guess ^^<\/li>\r\n<\/ul>\r\nIf there are more than one zero, repeat the second step.\r\n<h2>Solving Polynomial Equations and Inequalities on TI-84 Plus CE<\/h2>\r\nFirst, move all terms to the lefthand side of equal sign or inequality symbol. Then express the given equation or inequality as [latex]y = 0, y \\geq 0, y &gt; 0, y \\leq 0, or y &lt; 0[\/latex].\r\n\r\nSecond, set \"[latex]y[\/latex] = (lefthand side of the equation or inequality)\"\r\n\r\n<img class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" \/><img class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" \/>\u00a0Third, graph the function on TI=-84 using the \"y=\" button and the \"graph\" button.\r\n\r\nFourth, find the distinct parts of the graph:\r\n<ul>\r\n \t<li>If [latex]y&gt;0[\/latex], above the [latex]x[\/latex]-axis.<\/li>\r\n \t<li>If [latex]y=0[\/latex], on the [latex]x[\/latex]-axis.<\/li>\r\n \t<li>If [latex]y&lt;0[\/latex], below the [latex]x[\/latex]-axis.<\/li>\r\n<\/ul>\r\nLastly, find the interval(s) of [latex]x[\/latex] values where the part you found in the previous step. It is the solution of the equation or inequality.\r\n<h2><a id=\"Using Matrices in TI\"><\/a>Using Matrices to Solve Linear System on TI-84 Plus CE<\/h2>\r\nFirst, find the augmented matrix of the linear system.\r\n\r\n<img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" \/>\u00a0<span style=\"font-size: 1rem; text-align: initial;\">Second, to type in the augmented matrix into TI-84 Plus CE,\u00a0<\/span>press the \"2nd\" button and the \"[latex]x^(-1)[\/latex] button, which is \"matrix.\" Then go to\u00a0<span style=\"font-size: 1em;\">Matrix&gt; EDIT&gt; 1: [A].<\/span>\r\n<ul>\r\n \t<li>Type in the dimension of the matrix (# of rows X # of columns).<\/li>\r\n \t<li>Type in the entries.<\/li>\r\n \t<li><img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1128 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Quit.png\" alt=\"TI-84 Key: Quit\" width=\"73\" height=\"76\" \/>\u00a0When you are done with typing in entries, don't forget to \"quit\" using the \"2nd\" button and the \"mode\" button.<\/li>\r\n<\/ul>\r\n<img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" \/>\u00a0Third, to see the matrix you typed in, go to \"matrix\" using the \"2nd\" button and the\u00a0\"[latex]x^(-1)[\/latex]\" button. Then go to Matrix &gt; NAMES &gt; 1: [A].\r\n\r\n<img class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" \/>\u00a0Fourth, to find \"rref\" (reduced row echelon form),\u00a0go to \"matrix\" using the \"2nd\" button and the\u00a0\"[latex]x^(-1)[\/latex]\" button. Then go to Matrix &gt; MATH&gt; B: rref. Now go back to \"matrix.\" This time go to Matrix&gt; NAMES&gt; 1:[A] and then close the parenthesis \").\"\r\n\r\n<img class=\"size-full wp-image-1124 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" \/><img class=\" wp-image-1130 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Memory.png\" alt=\"TI-84 Key: Quit\" width=\"65\" height=\"70\" \/>\u00a0Lastly, to clear matrices in TI-84 Plus CE, go to \"memory\" using the \"2nd\" button and the \"+\" button. Then go to Memory&gt; 2: Mem MAnagement\/Delete&gt; 5: Matrix. Click \"del\" to clear any matrix.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Graphing a Function on TI-84 Plus CE<\/li>\n<li>Finding a Minimum\/Maximum Value on TI-84 Plus CE<\/li>\n<li>Finding Zeros on TI-84 Plus CE<\/li>\n<li>Solving Polynomial Equations and Inequalities on TI-84 Plus CE<\/li>\n<li>Using Matrices to Solve Linear System on TI-84 Plus CE<\/li>\n<\/ul>\n<\/div>\n<h2>Graphing a Function on TI-84 Plus CE<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y-65x48.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0First, to type in a function, press the &#8220;y=&#8221; button.<\/p>\n<ul>\n<li>Type in the given function as is. If the function is a rational function, please don\u2019t forget to put parentheses around its numerator and denominator or use the fraction form.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1120 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_X-T-Theta-n.png\" alt=\"TI-84 Key: X, T, theta, n\" width=\"67\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_X-T-Theta-n.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_X-T-Theta-n-65x49.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/>\u00a0To type [latex]x[\/latex], use &#8220;X, T, [latex]\\theta[\/latex], n&#8221; button.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1123 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Window.png\" alt=\"TI-84 Key: Window\" width=\"69\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Window.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Window-65x48.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0Second, to change the view of the function, press the &#8220;Window&#8221; button.<\/p>\n<ul>\n<li><span style=\"font-size: 1em;\">If the window is given, please change the window: [Xmin, Xmax, Xscl] X [Ymin, Ymax, Yscl]\u00a0<\/span><\/li>\n<li>Default window is [-10, 10, 1] X [-10, 10, 1]<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1118 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph-65x51.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0Third, to see the graph of the function, press the &#8220;Graph&#8221; button.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1122 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Zoom.png\" alt=\"TI-84 Key: Zoom\" width=\"67\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Zoom.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Zoom-65x49.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/>\u00a0Lastly, if you want to go back to the default window setting, press the &#8220;Zoom&#8221; button. Then choose &#8220;#6: ZStandard&#8221;<\/p>\n<h2>Finding a Minimum\/Maximum Value on TI-84 Plus CE<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y-65x48.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph-65x51.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0First, graph the function on TI=-84 using the &#8220;y=&#8221; button and the &#8220;graph&#8221; button.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1117 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png\" alt=\"TI-84 Key: Calc\" width=\"70\" height=\"79\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png 70w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc-65x73.png 65w\" sizes=\"auto, (max-width: 70px) 100vw, 70px\" \/>\u00a0Second, to find the minimum or maximum (or vertex or turning point) of the function, press the &#8220;2nd&#8221; button and the &#8220;trace&#8221; button in order, which is the &#8220;calc&#8221; button. Then choose <strong>&#8220;<span style=\"font-size: 1em;\">#3: minimum or #4: maximum.&#8221;<\/span><\/strong><\/p>\n<ul>\n<li><span style=\"font-size: 1em;\">Left Bound [latex]\\rightarrow[\/latex] click on the left side of the minimum\/maximum point<\/span><\/li>\n<li>Right Bound [latex]\\rightarrow[\/latex] click on the right side of the minimum\/maximum point<\/li>\n<li>Guess [latex]\\rightarrow[\/latex] optional; don\u2019t need to guess ^^<\/li>\n<\/ul>\n<div class=\"textbox\">\n<p>Somehow TI often shows some strange decimals. In that case, please round the number and check if it is working for the function.<\/p>\n<p>For example, given [latex]f(x)=x^2+2x-6[\/latex],\u00a0TI shows minimum [latex]x=-.9999994, y=-7[\/latex].<br \/>\nSo, the vertex (or minimum) is [latex](-1, -7)[\/latex].<br \/>\nTo check, plug in.\u00a0[latex]f(-1)=(-1)^2+2(-1)-6=1-2-6=-7[\/latex] [It works!]<\/p>\n<\/div>\n<h2>Finding Zeros on TI-84 Plus CE<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y-65x48.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph-65x51.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0First, graph the function on TI=-84 using the &#8220;y=&#8221; button and the &#8220;graph&#8221; button.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1117 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png\" alt=\"TI-84 Key: Calc\" width=\"70\" height=\"79\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc.png 70w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Calc-65x73.png 65w\" sizes=\"auto, (max-width: 70px) 100vw, 70px\" \/>\u00a0Second, to find the real zero (or [latex]x[\/latex]-intercept) of the function, press the &#8220;2nd&#8221; button and the &#8220;trace&#8221; button in order, which is the &#8220;calc&#8221; button. Then choose <strong>&#8220;<span style=\"font-size: 1em;\">#2: zero.&#8221;<\/span><\/strong><\/p>\n<ul>\n<li><span style=\"font-size: 1em;\">Left Bound [latex]\\rightarrow[\/latex] click on the left side of the minimum\/maximum point<\/span><\/li>\n<li>Right Bound [latex]\\rightarrow[\/latex] click on the right side of the minimum\/maximum point<\/li>\n<li>Guess [latex]\\rightarrow[\/latex] optional; don\u2019t need to guess ^^<\/li>\n<\/ul>\n<p>If there are more than one zero, repeat the second step.<\/p>\n<h2>Solving Polynomial Equations and Inequalities on TI-84 Plus CE<\/h2>\n<p>First, move all terms to the lefthand side of equal sign or inequality symbol. Then express the given equation or inequality as [latex]y = 0, y \\geq 0, y > 0, y \\leq 0, or y < 0[\/latex].\n\nSecond, set &#8220;[latex]y[\/latex] = (lefthand side of the equation or inequality)&#8221;\n\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1121 alignnone\" style=\"font-size: 1rem; orphans: 1; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png\" alt=\"TI-84 Key: y=\" width=\"69\" height=\"51\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_y-65x48.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1118 alignnone\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png\" alt=\"TI-84 Key: Graph\" width=\"69\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph.png 69w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Graph-65x51.png 65w\" sizes=\"auto, (max-width: 69px) 100vw, 69px\" \/>\u00a0Third, graph the function on TI=-84 using the &#8220;y=&#8221; button and the &#8220;graph&#8221; button.<\/p>\n<p>Fourth, find the distinct parts of the graph:<\/p>\n<ul>\n<li>If [latex]y>0[\/latex], above the [latex]x[\/latex]-axis.<\/li>\n<li>If [latex]y=0[\/latex], on the [latex]x[\/latex]-axis.<\/li>\n<li>If [latex]y<0[\/latex], below the [latex]x[\/latex]-axis.<\/li>\n<\/ul>\n<p>Lastly, find the interval(s) of [latex]x[\/latex] values where the part you found in the previous step. It is the solution of the equation or inequality.<\/p>\n<h2><a id=\"Using Matrices in TI\"><\/a>Using Matrices to Solve Linear System on TI-84 Plus CE<\/h2>\n<p>First, find the augmented matrix of the linear system.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png 73w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix-65x64.png 65w\" sizes=\"auto, (max-width: 73px) 100vw, 73px\" \/>\u00a0<span style=\"font-size: 1rem; text-align: initial;\">Second, to type in the augmented matrix into TI-84 Plus CE,\u00a0<\/span>press the &#8220;2nd&#8221; button and the &#8220;[latex]x^(-1)[\/latex] button, which is &#8220;matrix.&#8221; Then go to\u00a0<span style=\"font-size: 1em;\">Matrix&gt; EDIT&gt; 1: [A].<\/span><\/p>\n<ul>\n<li>Type in the dimension of the matrix (# of rows X # of columns).<\/li>\n<li>Type in the entries.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1128 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Quit.png\" alt=\"TI-84 Key: Quit\" width=\"73\" height=\"76\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Quit.png 75w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Quit-65x68.png 65w\" sizes=\"auto, (max-width: 73px) 100vw, 73px\" \/>\u00a0When you are done with typing in entries, don&#8217;t forget to &#8220;quit&#8221; using the &#8220;2nd&#8221; button and the &#8220;mode&#8221; button.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png 73w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix-65x64.png 65w\" sizes=\"auto, (max-width: 73px) 100vw, 73px\" \/>\u00a0Third, to see the matrix you typed in, go to &#8220;matrix&#8221; using the &#8220;2nd&#8221; button and the\u00a0&#8220;[latex]x^(-1)[\/latex]&#8221; button. Then go to Matrix &gt; NAMES &gt; 1: [A].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1119 alignnone\" style=\"orphans: 1;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png\" alt=\"TI-84 Key: Matrix\" width=\"73\" height=\"72\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix.png 73w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Matrix-65x64.png 65w\" sizes=\"auto, (max-width: 73px) 100vw, 73px\" \/>\u00a0Fourth, to find &#8220;rref&#8221; (reduced row echelon form),\u00a0go to &#8220;matrix&#8221; using the &#8220;2nd&#8221; button and the\u00a0&#8220;[latex]x^(-1)[\/latex]&#8221; button. Then go to Matrix &gt; MATH&gt; B: rref. Now go back to &#8220;matrix.&#8221; This time go to Matrix&gt; NAMES&gt; 1:[A] and then close the parenthesis &#8220;).&#8221;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1124 alignnone\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png\" alt=\"TI-84 Key: 2nd\" width=\"67\" height=\"54\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd.png 67w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_2nd-65x52.png 65w\" sizes=\"auto, (max-width: 67px) 100vw, 67px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1130 alignnone\" style=\"font-size: 1em;\" src=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Memory.png\" alt=\"TI-84 Key: Quit\" width=\"65\" height=\"70\" srcset=\"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Memory.png 73w, https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-content\/uploads\/sites\/5858\/2023\/07\/TI_Memory-65x69.png 65w\" sizes=\"auto, (max-width: 65px) 100vw, 65px\" \/>\u00a0Lastly, to clear matrices in TI-84 Plus CE, go to &#8220;memory&#8221; using the &#8220;2nd&#8221; button and the &#8220;+&#8221; button. Then go to Memory&gt; 2: Mem MAnagement\/Delete&gt; 5: Matrix. Click &#8220;del&#8221; to clear any matrix.<\/p>\n","protected":false},"author":705214,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1114","chapter","type-chapter","status-publish","hentry"],"part":115,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1114","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/705214"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1114\/revisions"}],"predecessor-version":[{"id":1236,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1114\/revisions\/1236"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/115"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1114\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=1114"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1114"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1114"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=1114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}