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) = 5x^2 − 10x + 7
h(x) = (pictured below)

Answer 1

These are all parabolas that open up or down, so the axis of symmetry is the vertical line\[x=x-coordinate~of~vertex\]
\(f(x)=-2(x-4)^2+2\) is in vertex form \(f(x)=a(x-h)^2+k\). The vertex is \((h,k)\) in general, an \((4,2)\) for your function. The axis of symmetry is \(x=h\), or \(x=4\) for your function.

For g(x), you can complete the square and write it in vertex form. Or you can use the formula \(x=-\frac{ b }{ 2a }\), where a and b come from the coefficients of \(g(x)=ax^2+bx+c\).