Section 3.1

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3.1 – Quadratic Functions A quadratic function is a any function of the form 2 ( ) f x ax bx c ! " " , where a is not equal to zero. The graph of a quadratic function is called a parabola. Parabolas look bowl or cup shaped. It will open up if a is positive and down if a is negative. The turning point of the parabola is called the vertex . The vertical line that bisects the graph through the vertex is called the axis of symmetry . The y -coordinate of the vertex represents the minimum value of the function if the graph opens up and the maximum value of the function if the graph opens down. Analyzing Quadratic Functions If the function is written in the form 2 ( ) f x ax bx c ! " " : 1. Find the vertex using the formula # # \$ % & & ( # \$ % & ( ) ) a b f a b 2 , 2 . 2. The axis of symmetry has the equation 2 b x a ! ) . 3. The min or max value will be equal to # \$ % & ( ) a b f 2 . ! Example 1 Given the function 2 ( ) 2 3 f x x x ! ) ) , find the vertex, axis of symmetry, min/max value, and sketch the graph. "

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If the function is written in transformational (standard) form k h x a y " ) ! 2 ) ( : 1. The vertex will be located at the point
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