y = ax 2 + bx + c Quadratic Equation Quadratic T erm Constant T erm Objective - To transform quadratic functions. a +a opens up -a opens down skinny parabola a > 1 wide parabola 0 < a < 1 c +c shifts up -c shifts down y-intercept y Graph f ( x ) = x 2 x y -3 2 9 4 x -2 -1 0 1 2 3 4 1 0 1 4 9 Vertex (0,0) Axis of Symmetry x = 0 y Graph f ( x ) = x 2 − 5 x y -3 -2 1 −3 ( ) 2 − 5 = 4 −2 ( ) 2 − 5 =−1 1 ( ) 2 5 4 x -1 0 1 2 3 Vertex (0,-5) Axis of Symmetry x = 0 −1 ( ) − 5 =−4 0 () 2 − 5 =−5 1 () 2 − 5 =−4 2 () 2 − 5 =−1 3 () 2 − 5 = 4 y Graph f ( x ) =− x 2 + 4 x y -3 -2 1 Vertex (0,4) Axis of Symmetry x = 0 −−3 ( ) 2 + 4 = −5 −−2 ( ) 2 + 4 = 0 1 ( ) 2 + 4 3 x -1 0 1 2 3 − −1 ( ) + 4 = 3 − 0 ( ) 2 + 4 = 4 − 1 ( ) 2 + 4 = 3 − 2 ( ) 2 + 4 = 0 − 3 ( ) 2 + 4 = −5 Translations of Quadratic Functions y Horizontal Translation 2 ( ) ( ) f x h h x f ( x ) = x 2 x ( ) ( ) − = − f x h h x h < 0 moves left h > 0 moves right Translations of Quadratic Functions y Vertical Translation 2 () + k fx x k f ( x ) = x 2 x () − = + k fx x k k < 0 moves down k > 0 moves up Lesson 5-1 Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010