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Graphs of Quadratic Functions Parabolas -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 -3 -2 -1 1 2 3 4 5 6 7 8 9 x y -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 -3 -2 -1 1 2 3 4 5 6 7 8 9 x y Minimum Vertex Axis of symmetry Maximum 2 ( ) f x ax bx c = + +

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2 Quadratic functions are any function of the form f(x)=ax +bx+c where a 0, and a,b and c are real numbers. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups. Para bolas are symmetic with respect to a line called the axis of symmetry. If a parabola is folded along its axis of symmetry, the two halves match exactly.
Graphing Quadratic Functions in Standard Form

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Seeing the Transformations

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Using Standard Form 2 finding the y intercept let x=0 y=-2(0-3) 8 y=-10 (0,-10) + -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 x y 2 ( ) 2( 3) 8 f x x = - - + ( , ) V(3,8) vertex h k axis of symmetry x=3 2 2 2 2 finding the x intercept, let y=0 0=-2(x-3) 8 8 2( 3) 2 2 4 ( 3) 4 ( 3) 2 3 3 2 , (5,0) (1,0) x x x x x + - - - = - - = - ± = - ± = - ± = a<0 so parabola has a minimum, opens down
Example Graph the quadratic function f(x) = - (x+2) 2 + 4.

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