Question

How do you write `f(x)= -x^2+6x-13` into vertex form?

Answer 1

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

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"`

`f(x)=-(x^2-6x+13)`

`color(white)(f(x))=-(x^2-6x+9-9+13)`

`color(white)(f(x))=-((x-3)^2+4)`

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