Question

What is the vertex of `y=2(x -1)^2 +3-x`?

Answer 1

Thus the vertex`->(x,y)=(5/4,15/8)`

Explanation:

`color(red)("For a full explanation of completing the square method see:")`
https://socratic.org/s/aDHYWAiE

We need to include the `x` that is outside the brackets

Expanding the brackets we have:
`y=2(x-1)^2" "color(white)(.)+3+x`
`y=2x^2-4x+2+3-x`

`y=2x^2-5x+5`

As the question presents a part vertex form equation it is reasonable to assume that the questioner's intention is for you to continue using vertex form format.

`y=2(x^2-5/2x)+5+k`

Where `k` is a correction constant

`y=2(x-5/4)^2+5+k`

Set `" "2(-5/4)^2+k=0" "=>" "k=-25/8` giving:

`y=2(x-5/4)^2+5-25/8`

`y=2(x-5/4)^2+15/8`

Thus the vertex`->(x,y)=(5/4,15/8)`