In the vertex form y = a(x - h)^2 + k, the vertex is at what point?

In the vertex form y = a(x - h)^2 + k, the vertex is at what point?

• A. (0, 0)
• B. (a, h)
• C. (h, 0)
• D. (h, k)

Answer: (D)

In this form, the parabola is built by shifting the basic parabola y = ax^2: it moves h units to the right and k units up. The vertex occurs when the squared term is zero, which happens at x = h, and then y = k. So the vertex is (h, k). The coefficient a only affects the direction and width of the parabola, not the location of the vertex. That’s why the other options don’t generally describe the vertex: the first coordinate is h and the second is k, not a or zero unless those shifts are specifically zero.

In this form, the parabola is built by shifting the basic parabola y = ax^2: it moves h units to the right and k units up. The vertex occurs when the squared term is zero, which happens at x = h, and then y = k. So the vertex is (h, k). The coefficient a only affects the direction and width of the parabola, not the location of the vertex.

That’s why the other options don’t generally describe the vertex: the first coordinate is h and the second is k, not a or zero unless those shifts are specifically zero.