Question

How do you rewrite p(x)=-5x2+120x-315 in vertex form

Answer 1

`p(x)=-5(x-12)^2+405`

Explanation:

Hi there!

Vertex form:
`f(x)=a(x-h)^2+k`

`p(x)=-5x^2+120x-315`

Factor out -5 from the first two terms

`p(x)=-5(x^2-24x)-315`

Complete the square by adding
`((24)/(2) )^2` (the square of half of the x-coefficient)

`p(x)=-5(x^2-24x+((24)/(2) )^2)-315-(-5)((24)/(2) )^2`

We're subtracting
`(-5)((24)/(2) )^2` because we need to keep the equation balanced and we can't just add new values.

Complete the square

`p(x)=-5(x-((24)/(2) ))^2-315-(-5)((24)/(2) )^2`

Simplify

`p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405`

Summary:

1. Complete the square
2. Simplify

I hope this helps!