Complete the square to rewrite y=x^2+8x+7 in vertex form and then identify the minimum y value of the function

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/ subtract (half the coefficient of the x- term)² to x² + 8x

y = x² + 2(4)x + 4² - 4² + 7 ← complete the square

  = (x + 4)² - 16 + 7

  = (x + 4)² - 9 ← in vertex form

with vertex = (- 4, - 9)

The minimum value is the y value of the vertex

Minimum value = - 9 when x = - 4

the answer to the expression is 83