Final answer:
The coordinates of the vertex of the parabola y = x² + 6x + 12 are (-3, 3), found using the vertex formula.
Step-by-step explanation:
The coordinates of the vertex of the parabola described by the equation y = x² + 6x + 12 can be found by completing the square or using the vertex formula for a quadratic equation, which is h = -b/(2a) and k = f(h), where a, b, and c are coefficients from the quadratic equation in the form ax² + bx + c.
To find the x-coordinate of the vertex (h), use the formula with our a equal to 1 and b equal to 6:
h = -6 / (2*1) = -3
To find the y-coordinate of the vertex (k), substitute h back into the equation:
k = (-3)² + 6*(-3) + 12 = 9 - 18 + 12 = 3
Therefore, the coordinates of the vertex are (-3, 3).