Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
f(x) = –2(x − 4)2 + 2

g(x) = 5x2 − 10x + 7

The graph is h(x)

Answer 1

for f(x) = -2(x-4)2+2 - set equation to y = -2(x-4)2+2, solve x-4=0, x = 4

axis of symmetry is x = 4

for g(x) = 5x2-10x+7, set equation to y = 5x2-10x+7, solve the square: 5x2 becomes 5(x-1)2 solve x-1 = 0, x = 1

 axis of symmetry is x=1

 for H(x) what x value would be the centerline so that the graph symmetry is the same on both sides? looking at the graph the top of the arc is on -2

 so axis of symmetry is x = -2