Answer:
g(x) = - 2(x - 5)² + 1
Step-by-step 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
