Consider the relation y = 4|x + 2| + 7. What are the coordinates of the vertex?

(7, - 2)

(2, 7)

(4, - 2)

(-2, 7)

To answer, we set the expression inside the absolute value symbol (II) equal to 0. That is,

x + 2 = 0

Then, we solve for the value of x.

x + 2 - 2 = 0 - 2

Hence, the value of x from the equation above is equal to - 2.

Then, substitute the value of x to the equation and drop the absolute value symbol.

y = 4 (x + 2) + 7

Substituting,

y = 4 (-2 + 2) + 7

y = 4 (0) + 7

y = 7

Thus, the vertex of the absolute value equation is equal to (-2,7). The answer is the last choice.