Question

What is the vertex form of `y= x^2 – 5x – 6`?

Answer 1

`y=(x-5/2)^2-49/4`

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"`

add `(1/2" coefficient of x-term")^2" to " x^2-5x`

Since we are adding a value which is not there we must also subtract this value.

`"add / subtract " (-5/2)^2=25/4`

`y=(x^2-5xcolor(red)(+25/4))color(red)(-25/4)-6`

`color(white)(y)=(x-5/2)^2-49/4larrcolor(red)" in vertex form"`