Question

How do you write `f(x) = x^2+2x-8` in vertex form?

Answer 1

vertex form: `(x-color(red)(color(white)("")(-1)))^2+color(blue)(color(white)("")(-9))` with vertex at `(color(red)(-1),color(blue)(-9))`

Explanation:

General vertex form:
`color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)` with vertex at `(color(red)(a),color(blue)(b))`

`f(x)=x^2+2x-8`

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

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

`rarr f(x)=color(green)(1)(x-color(red)(color(white)("")(-1)))^2+color(blue)(""(-9))color(white)("XXX")` (in complete vertex form)