Question

What is the vertex of the quadratic function Y = –3x² – 12?

1) (0, 0)
2) (0, -12)
3) (0, 12)
4) (12, 0)

Answer 1

The vertex of the quadratic function Y = –3x² – 12 is at (0, -12), since the x-coordinate of the vertex is found using x = -b/2a, which is 0 in this case, and substituting x = 0 into the function gives the y-coordinate.

Step-by-step explanation:

The question asks about finding the vertex of the quadratic function Y = –3x² – 12. A vertex of a quadratic function in standard form, which is y = ax² + bx + c, can be found using the vertex formula (-b/2a, f(-b/2a)). However, since our function is missing the x term (or b = 0), the vertex will occur at x = 0. Plugging x = 0 into the equation, we find the y-coordinate: Y = –3(0)² – 12 = -12. Therefore, the vertex of the quadratic function is at (0, -12), which corresponds to option 2.