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PP Section 4.2

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A quadratic function is a function of the form: f x ax bx c ( ) = + + 2 where a , b , and c are real numbers and a 0. The domain of a quadratic function consists of all real numbers. The graph of a quadratic function is called a parabola.
Examples of quadratic functions: 2 3 ) ( , 1 3 2 ) ( 2 2 - + - = + - = x x x g x x x f

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Graphs of a quadratic function f ( x ) = ax 2 + bx + c, a 0 a > 0 Opens up Vertex is lowest point Axis of symmetry a < 0 Opens down Vertex is highest point Axis of symmetry
To graph a quadratic function is equivalent to graphing a parabola. k h x a y c bx ax y + - = + + = 2 2 ) ( form standard in equation put the to need first we , graph To . 0 if down and 0 if up opens parabola the , is symmetry of axis the ), , ( point the is parabola the of vertex The < = = a a h x k h V

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THE GRAPH OF QUADRATIC FUNCTION y =f(x) Vertex = (h , k) Axis of Symmetry: x = h f(x) = a(x - h) 2  + k, a > 0
Example Graph f(x) = - (x + 1) Graph f(x) = - (x + 1)

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