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