Question

What is the vertex form of `y=2x^2 + 4x + 46`?

Answer 1

`y=2(x+1)^2+44`

Explanation:

The equation of a parabola in `color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where(h ,k) are the coordinates of the vertex and a is a constant.

We can obtain vertex form by `color(blue)"completing the square"`

`y=2(x^2+2x+23)`

`color(white)(x)=2(x^2+2xcolor(red)(+1)color(red)(-1)+23)`

`color(white)(x)=2((x+1)^2+22)`

`rArry=2(x+1)^2+44larrcolor(red)" in vertex form"`