Question

How do you write the vertex form equation of the parabola `y = x^2 - 4x + 12`?

Answer 1

`y= (x-2)^2 +8`

Explanation:

`y = {x^2 - 2*2x +(2)^2} -(2)^2 +12`
Changing it to `( a^2 +2ab + b^2 )` form to convert it to `(a+b)^2`
`y = (x-2)^2 - 4 +12`
`y= (x-2)^2 +8` is the vertex form.

Answer 2

`y-8=(x-2)^2`

Explanation:

`y=x^2-4x+12`

`=x^2-2xx2xx x+2^2-4+12`

`=(x-2)^2+8`

As in an equation of the vertex form `y-k=a(x-h)^2` or `y=(x-h)^2+k` the vertex is `(h,k)`

here we have vertex at `(2,8)` and vertex form of equation is `y-8=(x-2)^2`

graph{x^2-4x+12 [-8.24, 11.76, 6.08, 16.08]}