(Free to use. May not be sold) Year 12 - General Quadratic Functions Press ‘Ctrl-A’ © G Dear 2009 (Free to use. May not be sold) 1

Quadratic Functions (1/6) The independent variable has a power of 2. The dependent variable has a power of 1. y = ax2 + bx +c 1 1 When graphed they appear as a parabolic graph. 2

Quadratic Function y = x2 (2/6) -3 -2 -1 -½ ½ 1 2 3 y 9 4 1 ¼ ¼ 1 4 9 9 7 5 3 1 2 -1 -2 -3 x y y=x2 Parabola 3

Quadratic Function y = x2 (3/6) -3 -2 -1 ½ 1 2 3 y 9 4 1 ¼ ¼ 1 4 9 In this course we don’t use negative values for x. 4

Quadratic Function y = x2 (3/6) ½ 1 2 3 y ¼ 1 4 9 9 7 5 3 1 2 x y y=x2 5

Quadratic Function y = 2x2 - 4x + 5 (4/6) 1 2 3 4 y 5 3 5 11 21 20 16 12 8 4 1 2 3 x y y=2x2-4x+5 6

Quadratic Function y = -x2 + 3x + 5 (5/6) 1 2 3 4 y 5 7 7 5 1 10 8 6 4 2 1 3 x y y=-x2+3x+5 7

Quadratic Function h = 20t – 5t2 (6/6) Throwing a ball vertically h = ut + ½at2 What is the maximum height? t 1 2 3 4 h 15 20 15 20 20 16 12 8 4 1 2 3 t h h=20t-5t2 8