4-1 Quadratic Functions and Transformations

Objective

To identify and graph quadratic functions

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In the Solve It, you used the parabolic shape of the horse's jump. A parabola is the graph of a quadratic function, which you can write in the form f ( x ) = a x 2 + b x + c , f open x close equals eh , x squared , plus b x plus c comma  where a ≠ 0 . eh not equal to 0 .

Essential Understanding The graph of any quadratic function is a transformation of the graph of the parent quadratic function, y = x 2 . y equals , x squared , .

The vertex form of a quadratic function is f ( x ) = a ( x − h ) 2 + k , f open x close equals eh . open x minus h close squared . plus k comma  where a ≠ 0 . eh not equal to 0 .  The axis of symmetry is a line that divides the parabola into two mirror images. The equation of the axis of symmetry is x = h. The vertex of the parabola is (h, k), the intersection of the parabola and its axis of symmetry.

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