Question

What is the vertex form of `y=x^2-5x-13`?

Answer 1

`y=(x-5/2)^2-77/4`

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 multiplier"`

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

`y=x^2+2(-5/2)x color(red)(+25/4)color(red)(-25/4)-13`

`color(white)(y)=(x-5/2)^2-77/4larrcolor(red)"in vertex form"`