{"id":1923,"date":"2015-11-12T18:30:43","date_gmt":"2015-11-12T18:30:43","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1923"},"modified":"2015-11-12T18:30:43","modified_gmt":"2015-11-12T18:30:43","slug":"key-concepts-glossary-23","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-23\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Equations<\/h2>\n<table id=\"fs-id1483252\" summary=\"..\"><tbody><tr><td>Parabola, vertex at origin, axis of symmetry on <em>x<\/em>-axis<\/td>\n<td>[latex]{y}^{2}=4px[\/latex]<\/td>\n<\/tr><tr><td>Parabola, vertex at origin, axis of symmetry on <em>y<\/em>-axis<\/td>\n<td>[latex]{x}^{2}=4py[\/latex]<\/td>\n<\/tr><tr><td>Parabola, vertex at [latex]\\left(h,k\\right)[\/latex], axis of symmetry on <em>x<\/em>-axis<\/td>\n<td>[latex]{\\left(y-k\\right)}^{2}=4p\\left(x-h\\right)[\/latex]<\/td>\n<\/tr><tr><td>Parabola, vertex at [latex]\\left(h,k\\right)[\/latex], axis of symmetry on <em>y<\/em>-axis<\/td>\n<td>[latex]{\\left(x-h\\right)}^{2}=4p\\left(y-k\\right)[\/latex]<\/td>\n<\/tr><\/tbody><\/table><h2>Key Concepts<\/h2>\n<ul><li>A parabola is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.<\/li>\n\t<li>The standard form of a parabola with vertex [latex]\\left(0,0\\right)[\/latex] and the <em>x<\/em>-axis as its axis of symmetry can be used to graph the parabola. If [latex]p&gt;0[\/latex], the parabola opens right. If [latex]p&lt;0[\/latex], the parabola opens left.<\/li>\n\t<li>The standard form of a parabola with vertex [latex]\\left(0,0\\right)[\/latex] and the <em>y<\/em>-axis as its axis of symmetry can be used to graph the parabola. If [latex]p&gt;0[\/latex], the parabola opens up. If [latex]p&lt;0[\/latex], the parabola opens down.<\/li>\n\t<li>When given the focus and directrix of a parabola, we can write its equation in standard form.<\/li>\n\t<li>The standard form of a parabola with vertex [latex]\\left(h,k\\right)[\/latex] and axis of symmetry parallel to the <em>x<\/em>-axis can be used to graph the parabola. If [latex]p&gt;0[\/latex], the parabola opens right. If [latex]p&lt;0[\/latex], the parabola opens left.<\/li>\n\t<li>The standard form of a parabola with vertex [latex]\\left(h,k\\right)[\/latex] and axis of symmetry parallel to the <em>y<\/em>-axis can be used to graph the parabola. If [latex]p&gt;0[\/latex], the parabola opens up. If [latex]p&lt;0[\/latex], the parabola opens down.<\/li>\n\t<li>Real-world situations can be modeled using the standard equations of parabolas. For instance, given the diameter and focus of a cross-section of a parabolic reflector, we can find an equation that models its sides.<\/li>\n<\/ul><h2>Glossary<\/h2>\n<dl id=\"fs-id1893659\" class=\"definition\"><dt>directrix<\/dt><dd id=\"fs-id1893662\">a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant<\/dd><\/dl><dl id=\"fs-id1893665\" class=\"definition\"><dt>focus (of a parabola)<\/dt><dd id=\"fs-id1893669\">a fixed point in the interior of a parabola that lies on the axis of symmetry<\/dd><\/dl><dl id=\"fs-id1893672\" class=\"definition\"><dt>latus rectum<\/dt><dd id=\"fs-id1893675\">the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola<\/dd><\/dl><dl id=\"fs-id1893679\" class=\"definition\"><dt>parabola<\/dt><dd id=\"fs-id1893682\">the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix<\/dd><\/dl>","rendered":"<h2>Key Equations<\/h2>\n<table id=\"fs-id1483252\" summary=\"..\">\n<tbody>\n<tr>\n<td>Parabola, vertex at origin, axis of symmetry on <em>x<\/em>-axis<\/td>\n<td>[latex]{y}^{2}=4px[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Parabola, vertex at origin, axis of symmetry on <em>y<\/em>-axis<\/td>\n<td>[latex]{x}^{2}=4py[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Parabola, vertex at [latex]\\left(h,k\\right)[\/latex], axis of symmetry on <em>x<\/em>-axis<\/td>\n<td>[latex]{\\left(y-k\\right)}^{2}=4p\\left(x-h\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Parabola, vertex at [latex]\\left(h,k\\right)[\/latex], axis of symmetry on <em>y<\/em>-axis<\/td>\n<td>[latex]{\\left(x-h\\right)}^{2}=4p\\left(y-k\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Key Concepts<\/h2>\n<ul>\n<li>A parabola is the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.<\/li>\n<li>The standard form of a parabola with vertex [latex]\\left(0,0\\right)[\/latex] and the <em>x<\/em>-axis as its axis of symmetry can be used to graph the parabola. If [latex]p>0[\/latex], the parabola opens right. If [latex]p<0[\/latex], the parabola opens left.<\/li>\n<li>The standard form of a parabola with vertex [latex]\\left(0,0\\right)[\/latex] and the <em>y<\/em>-axis as its axis of symmetry can be used to graph the parabola. If [latex]p>0[\/latex], the parabola opens up. If [latex]p<0[\/latex], the parabola opens down.<\/li>\n<li>When given the focus and directrix of a parabola, we can write its equation in standard form.<\/li>\n<li>The standard form of a parabola with vertex [latex]\\left(h,k\\right)[\/latex] and axis of symmetry parallel to the <em>x<\/em>-axis can be used to graph the parabola. If [latex]p>0[\/latex], the parabola opens right. If [latex]p<0[\/latex], the parabola opens left.<\/li>\n<li>The standard form of a parabola with vertex [latex]\\left(h,k\\right)[\/latex] and axis of symmetry parallel to the <em>y<\/em>-axis can be used to graph the parabola. If [latex]p>0[\/latex], the parabola opens up. If [latex]p<0[\/latex], the parabola opens down.<\/li>\n<li>Real-world situations can be modeled using the standard equations of parabolas. For instance, given the diameter and focus of a cross-section of a parabolic reflector, we can find an equation that models its sides.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1893659\" class=\"definition\">\n<dt>directrix<\/dt>\n<dd id=\"fs-id1893662\">a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant<\/dd>\n<\/dl>\n<dl id=\"fs-id1893665\" class=\"definition\">\n<dt>focus (of a parabola)<\/dt>\n<dd id=\"fs-id1893669\">a fixed point in the interior of a parabola that lies on the axis of symmetry<\/dd>\n<\/dl>\n<dl id=\"fs-id1893672\" class=\"definition\">\n<dt>latus rectum<\/dt>\n<dd id=\"fs-id1893675\">the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola<\/dd>\n<\/dl>\n<dl id=\"fs-id1893679\" class=\"definition\">\n<dt>parabola<\/dt>\n<dd id=\"fs-id1893682\">the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1923\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1923","chapter","type-chapter","status-publish","hentry"],"part":1904,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1923","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1923\/revisions"}],"predecessor-version":[{"id":2203,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1923\/revisions\/2203"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1904"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1923\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=1923"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1923"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1923"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=1923"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}