Question

How do you find the vertex of a parabola `f(x) = -x^2 + 2x + 5`?

Answer 1

Vertex is at `(1,6)`

Explanation:

A function expressed in the form
`color(white)("XXXX")` `f(x) = m(x-a)^2+b` is in "vertex form" with its vertex at `(a,b)`

One way of determining the vertex of a parabolic function is to convert it into "vertex form".

`f(x)=-x^2+2x+5`
`color(white)("XXXX")`extract `m`
`f(x) = (-1)(x^2-2x)+5`
`color(white)("XXXX")`complete the square
`f(x) = (-1)(x^2-2x+1) + 5 -(-1)(1)`
`color(white)("XXXX")`simplify into vertex form
`f(x) = (-1)(x-1)^2+6`
`color(white)("XXXX")`read the vertex coordinates from the form
Vertex is at `(1,6)`