Question

Write in the equation form g(x)= a(x-h)^2+k

for g(x)= -2x^2+20x-49

Please include steps of how you set it in equation form. THX

Answer 1

g(x) = - 2(x - 5)² + 1

Explanation:

g(x) = - 2x² + 20x - 49 ← factor out - 2 from the first two terms

g(x) = - 2(x² - 10x) - 49

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 10x

g(x) = - 2(x² + 2(- 5)x + 25 - 25) - 49

= - 2(x - 5)² + 50 - 49

= - 2(x - 5)² + 1