Question

(02.04 HC)

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x)
f(x) = -2(x-4)2 +2
X
-4-3-2
h(x)

Answer 1

For
`f(x)`, the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of
`f(x)` has coordinates
`(4,2)`. Thus, the axis of symmetry has equation
`x=4`.

Similarly, for
`h(x)`, the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates
`(-2,2)`. Thus, the axis of symmetry has equation
`x=-2`.