Question

What is the vertex of # y= 2x^2+4x-2?

Answer 1

vertex at `(-1,-4)`

Explanation:

Given: `y=2x^2+4x-2`
Convert the given form into "vertex form" `y=m(x-a)^2+b` with vertex at `(a,b)`

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

complete the square
`color(white)("XXX")y=2(x^2+2xcolor(red)(+1))-2color(red)(-2)`

`color(white)("XXX")y=2(x+1)^2-4`

`color(white)("XXX")y=2(x-(color(blue)(-1)))^2+(color(blue)(-4))`
which is the vertex form with vertex at `(color(blue)(-1),color(blue)(-4))`
graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0.7]}