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3.3 Quadratic Functions

3.3 Quadratic Functions - t s t f 2 2 b b f a a c...

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Quadratic Functions Quadratic Functions Section 3.3 Section 3.3
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Parabolas Parabolas The rule of a quadratic function is a polynomial of degree 2. The shape is a parabola. vertex x- intercepts
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Forms of a Quadratic Function Forms of a Quadratic Function Transformation form: Polynomial form: x-Intercept form: where a, b, c, h, k, s, and t are real numbers and a = 0. If a is positive, the graph opens upward. If a is negative, the graph opens downward. 2 ( ) ( ) f x a x h k = - + ( ) ( )( ) f x a x s x t = - - 2 ( ) f x ax bx c = + +
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Name Transformation Polynomial x-Intercept Form Vertex x- Intercept y- Intercept 2 ( ) ( ) f x a x h k = - + 2 ah k + 2 ( ) f x ax bx c = + + 2 4 2 b b ac a - ± - k h a - ± ( ) ( )( ) f x a x s x t = - - s and t ast ( , ) h k , 2 2 s
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Unformatted text preview: t s t f + + ÷ ÷ , 2 2 b b f a a -- ÷ ÷ c Applications Applications • In the graph of a quadratic function, the vertex of the parabola is either a maximum or a minimum of the function. Thus, the solution of many applications depends on finding the vertex of the parabola. Joke Time Joke Time • Why wouldn’t they let the butterfly into the dance? • Because it was a moth ball. • What happened when the chicken slept under the car? • She woke up oily next morning....
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3.3 Quadratic Functions - t s t f 2 2 b b f a a c...

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