Final answer:
The vertex of the parabola of the quadratic function y = x² + 8x +12 is at the point (-4, -4).
Step-by-step explanation:
The vertex of the parabola can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, the quadratic function is y = x² + 8x + 12, so a = 1, b = 8, and c = 12.
Using the formula, we can calculate x = -8/(2*1) = -4.
Substituting x = -4 into the equation, we can calculate y = (-4)² + 8(-4) + 12 = 16 - 32 + 12 = -4.
Therefore, the vertex of the parabola is at the point (-4, -4).