Question

What is the vertex of `y= 2(x-1)^2 +16`?

Answer 1

`(1,16)`

Explanation:

The vertex form of a parabola with a vertex at `(color(red)h,color(blue)k)` is

`y=a(x-color(red)h)^2+color(blue)k`

Notice that the equation `y=2(x-color(red)1)^2+color(blue)16` fits this mold exactly.

We can see by comparing the two that `h=1` and `k=16`, so the parabola's vertex is at the point `(h,k)rarr(1,16)`.

We can check a graph:

graph{2(x-1)^2+16 [-10, 10, -10, 50]}