Question

Given the functions f(x) = 3x2, g(x) = x2 - 4x + 5, and h(x) = -2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry

Answer 1

In order to find the vertex for each of these (what you need to help you find the axis of symmetry which is an "x=" equation) you have to complete the square on g(x) and h(x). f(x) is already as simplified as it's going to be and the axis of symmetry hasn't moved from the y-axis, so the axis of symmetry is x=0. Completing the square on g(x) puts it into the vertex form of (x-2)^2+1 = y and the axis of symmetry is x=2. Completing the square of h(x) puts it into the vertex form of -2(x-1)^2+3 = y and the axis of symmetry is x = 1. So putting them in order you have f(x) then h(x) and then g(x)