Question

How do you find the vertex for `y=x^2-10x+20`?

Answer 1

`color(green)("vertex: " (5,-5)`

Explanation:

The general vertex form for a parabola is
`color(white)("XXX")m(x-a)^2+b` with a vertex at `(a,b)`

Converting `y=x^2-10x+20` into vertex form:

Complete the square:
`color(white)("XXX")y=x^2-10x+5^2+20-5^2`

Simplify into vertex form
`color(white)("XXX")y=1(x-5)^2-5`
with vertex at `(5,-5)`
graph{x^2-10x+20 [-5.13, 14.87, -7.32, 2.68]}