Question

What is the vertex of `y=1/5(x/2-15)^2-2`?

Answer 1

vertex: `(30,-2)`

Explanation:

Our "target will be to convert the given equation into "vertex form":
`color(white)("XXX")y=m(x-color(red)(a))^2+color(blue)(b)` with vertex at `(color(red)(a),color(blue)(b))`

Given
`color(white)("XXX")y=1/2(x/2-15)^2-2`

`y=1/2((x-30)/2)^2-2`

`y=1/2(((x-30)^2)/(2^2))-2`

`y=1/8(x-color(red)(30))^2+color(blue)("("-2")")`

which is the vertex form with a vertex at `(color(red)(30),color(blue)(-2))`

The graph below may help to indicate that our answer is (at least approximately) correct:
graph{1/5(x/2-15)^2-2 [9.41, 49.99, -10.61, 9.69]}