Question

How do you find the vertex of `f(x)=-(x-1)^2+2`?

Answer 1

Vertex: `(1,2)`

Explanation:

An equation in the form `f(x)=color(green)(m)(x-color(red)(a))^2+color(blue)(b)`
is in vertex form with vertex at `(color(red)(a),color(blue)(b))`

`f(x)=-(x-1)^2+2`
is equivalent to
`f(x)=color(green)(""(-1))(x-color(red)(1))^2+color(blue)(2)`
and therefore has a vertex at `(color(red)(1),color(blue)(2))`

Here is a graph of the original equation for verification purposes:
graph{-(x-1)^2+2 [-2.507, 3.652, -0.54, 2.537]}