Lesson 25

Lesson 25 - Lesson 25 Quadratic Function: - a function is...

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Unformatted text preview: Lesson 25 Quadratic Function: - a function is quadratic if it is in any of the following forms: o () , where ( ) o () , where ( )( ), where o () - the degree of a quadratic function is _______ - the graph of a quadratic function a parabola Vertex of a parabola: - the turning point, the point where the graph of a quadratic function changes from increasing to decreasing, or vice versa - the -coordinate of the vertex is either the maximum or minimum function value - the -coordinate of the vertex is the input where the maximum or minimum function value occurs Example 1: Graph the following quadratic functions. List the vertex and any symmetry. a. ( ) b. ( ) b. ( ) The graph of a quadratic function is a parabola that opens up or down (why can’t it open to the left or right?). If the leading coefficient , the parabola opens up; if the leading coefficient , the parabola opens down (why can’t the leading coefficient ?). The graph of a quadratic function will always be symmetric about a vertical line called the line of symmetry. Example 2: Graph the following functions by transforming the graph of the function ( ) . Find the vertex of each and list any symmetry. ) ( ) a. ( ) ( b. ( ) c. ( ) Can you determine the vertex of each graph without graphing? Can you determine the line of symmetry for each graph without graphing? Standard Equation of a Parabola with Vertical Axis: ( ) ) - the vertex is ( - when , the parabola opens _______ - when , the parabola opens _______ - symmetric about the line , where is the -coordinate of the vertex When a quadratic function, such as () is written in the form of the standard equation of a parabola with a vertical axis ( ) the vertex is ( ), the line of symmetry is sketched by transforming the basic parabola units to the right and 2 units up). , and the graph can be (shift the graph 3 How can a quadratic function of the form ( ) ( ) converted to the form ( ) ? How can ( ) be written in the form be ( ) ? Example 3: Given the following functions, find the standard equation of the parabola, then graph and find the following: a. ( ) () () when b. ( ) () () when c. ( ) () () d. ( ) () () when ( when )( ) Example 4: Find the standard equations of the parabolas shown: a. b. c. d. Looking back at the graphs in previous two examples, do you notice a relationship between the -coordinate of the vertex and the -intercepts? Example 5: Find the standard equation of a parabola with a vertical axis that satisfies the given conditions: ) a. Vertex ( ), passing through ( b. Vertex ( c. -intercepts ), -intercept and , minimum value of ...
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