Question

How do you write `f(x) = −2x^2 − 4x + 7` in vertex form?

Answer 1

`f(x)=-2(x+1)^2+9`

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.

`"using the method of "color(blue)"completing the square"`

add `(1/2"coefficient of x-term")^2" to " x^2+2x`

Since we are adding a value that is not there we must also subtract the value.

`"that is add/subtract " (2/2)^2=1`

`-2(x^2+2x)+7larr" coefficient of " x^2" is unity"`

`=-2(x^2+2xcolor(red)(+1)color(red)(-1))+7`

`=-2(x+1)^2+2+7`

`rArrf(x)=-2(x+1)^2+9larrcolor(red)" in vertex form"`