Answer:
y = - 7(x + 5)² + 3
Explanation:
A quadratic function expressed in vertex form is
y = a(x - h)² + k
(h, k ) are the coordinates of the vertex and a is a multiplier
given
y = - 7x² - 70x - 172
Before completing the square we require the coefficient of the x² term to be 1.
factor out - 7 from the first 2 terms
y = - 7(x² + 10x) - 172
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 10x
y = - 7(x² + 2(5)x + 25 - 25) - 172
y = - 7(x + 5)² + (- 7)(- 25) - 172
y = - 7(x + 5)² + 175 - 172
y = - 7(x + 5)² + 3 ← in vertex form