Question

What is the vertex of `y=2(x-3)^2+4`?

Answer 1

`(3,4)`

Explanation:

This is in vertex form. Vertex form is a handy way of writing quadratic equations so that their vertices are evident from the equation itself and require no algebra to find.

Vertex form is:

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

When `(h,k)` is the vertex of the parabola.

The only tricky thing to watch out for is the `x`-coordinate. In vertex form, it's written as `-h`, so the actual `x`-coordinate `h` will be the opposite of whatever is written inside the square term.

Thus,

`h=3`
`k=4`

The vertex is at `(3,4)`.

graph{2(x-3)^2+4 [-8.02, 14.48, -1.53, 9.72]}