Question

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

Answer 1

Answer:

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

Step-by-step 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 $(\frac{24}{2} )^2$ (the square of half of the x-coefficient)

$p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2$

We're subtracting $(-5)(\frac{24}{2} )^2$ because we need to keep the equation balanced and we can't just add new values.

Complete the square

$p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2$

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!