Question

What is the vertex form of `y= 2x^2-10x+12`?

Answer 1

The vertex form is `y=2(x-5/2)^2-1/2`

Explanation:

`y=2x^2-10x+12`
Factorise partly, before completing the square
`y=2(x^2-5x)+12`
`y=2(x^2-5x+25/4)+12-25/2`
`y=2(x-5/2)^2-1/2`
When `x=0` `=>` `y=2*25/4-1/2=12`
when `y=0` `=>` `(x-5/2)^2=1/4`
`x-5/2=+-1/2` `=>` `x=2` or `x=3`
graph{2x^2-10x+12 [-0.493, 9.374, -2.35, 2.583]}