Question

What is the the vertex of `y=(x -5)^2 + 12x -36`?

Answer 1

vertex: `(x,y)= (-1,-12)`

Explanation:

Given
`color(white)("XXX")y=(x-5)^2+12x-36`

Convert into the general vertex form: `y=(x-a)^2+b` with vertex at `(a,b)`

`color(white)("XXX")y=(x^2-10x+25)+12x-36`

`color(white)("XXX")y=x^2+2x+1 -12`

`color(white)("XXX")y=(x+1)^2-12`

Graph of `y=(x-5)^2+12x-36`
graph{(x-5)^2+12x-36 [-6.696, 3.17, -12.26, -7.33]}