Question

How do you write `f(x)=-3x^2+24x-51` in vertex form?

Answer 1

`f(x)=-3(x-4)^2-3`

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.

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

`• " coefficient of "x^2" term must be unity"`

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

`f(x)=-3(x^2-8x+17)`

`color(white)(f(x))=-3(x^2-8xcolor(red)(+16)color(red)(-16)+17)`

`color(white)(f(x))=-3(x-4)^2-3larrcolor(red)" in vertex form"`