Question

How do you write `f(x) = x^2+ 8x- 5` in vertex form?

Answer 1

`f(x)=(x+4)^2-21`

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 multiplier"`

`"to obtain this form use the method of "color(blue)"completing the square"`

`• " ensure coefficient of "x^2" term is 1"`

`• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+8x`

`f(x)=x^2+8x-5larr" coefficient of "x^2" is 1"`

`color(white)(f(x))=x^2+2(4)xcolor(red)(+16)color(red)(-16)-5`

`color(white)(f(x))=(x+4)^2-21larrcolor(red)" in vertex form"`