Question

What is the vertex form of `y = x(x-5)+13`?

Answer 1

`y=(x-5/2)^2+27/4`

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(x-5)+13=x^2-5x+13`

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

`color(white)(y)=(x-5/2)^2+27/4larrcolor(red)"in vertex form"`