{"id":5307,"date":"2021-10-11T20:36:56","date_gmt":"2021-10-11T20:36:56","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lcudd-tulsacc-collegealgebra\/chapter\/summary-minima-and-maxima-of-quadratic-functions\/"},"modified":"2021-10-28T15:38:39","modified_gmt":"2021-10-28T15:38:39","slug":"summary-minima-and-maxima-of-quadratic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lcudd-tulsacc-collegealgebra\/chapter\/summary-minima-and-maxima-of-quadratic-functions\/","title":{"raw":"Summary: Analysis of Quadratic Functions","rendered":"Summary: Analysis of Quadratic Functions"},"content":{"raw":"
The zeros, or [latex]x[\/latex]-intercepts, are the points at which the parabola crosses the [latex]x[\/latex]-axis. The [latex]y[\/latex]-intercept is the point at which the parabola crosses the [latex]y[\/latex]-<\/em>axis.<\/li>\r\n \t
The vertex can be found from an equation representing a quadratic function.<\/li>\r\n \t
A quadratic function\u2019s minimum or maximum value is given by the [latex]y[\/latex]-value of the vertex.<\/li>\r\n \t
The minimum or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.<\/li>\r\n \t
Some quadratic equations must be solved by using the quadratic formula.<\/li>\r\n \t
The vertex and the intercepts can be identified and interpreted to solve real-world problems.<\/li>\r\n<\/ul>\r\n
Glossary<\/h2>\r\n
\r\n \t
vertex<\/strong><\/dt>\r\n \t
the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertex form of a quadratic function<\/strong><\/dt>\r\n \t
another name for the standard form of a quadratic function<\/dd>\r\n<\/dl>\r\n
\r\n \t
zeros<\/strong><\/dt>\r\n \t
in a given function, the values of [latex]x[\/latex] at which [latex]y=0[\/latex], also called roots<\/dd>\r\n<\/dl>","rendered":"
The zeros, or [latex]x[\/latex]-intercepts, are the points at which the parabola crosses the [latex]x[\/latex]-axis. The [latex]y[\/latex]-intercept is the point at which the parabola crosses the [latex]y[\/latex]–<\/em>axis.<\/li>\n
The vertex can be found from an equation representing a quadratic function.<\/li>\n
A quadratic function\u2019s minimum or maximum value is given by the [latex]y[\/latex]-value of the vertex.<\/li>\n
The minimum or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.<\/li>\n
Some quadratic equations must be solved by using the quadratic formula.<\/li>\n
The vertex and the intercepts can be identified and interpreted to solve real-world problems.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
vertex<\/strong><\/dt>\n
the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function<\/dd>\n<\/dl>\n
\n
vertex form of a quadratic function<\/strong><\/dt>\n
another name for the standard form of a quadratic function<\/dd>\n<\/dl>\n
\n
zeros<\/strong><\/dt>\n
in a given function, the values of [latex]x[\/latex] at which [latex]y=0[\/latex], also called roots<\/dd>\n<\/dl>\n\n\t\t\t \n\t\t\t