The coordinates (h, k) in the vertex form of a quadratic indicate which of the following?

• A. The vertex location, with h as the horizontal coordinate and k as the vertical coordinate
• B. The intercepts where the graph crosses the axes
• C. The slope at the vertex
• D. They are the coefficients of the quadratic terms

Answer: (B)

The key idea is that in vertex form y = a(x − h)² + k, the pair (h, k) marks the exact location of the parabola’s vertex. The horizontal shift h moves the graph left or right by h units, and the vertical shift k moves it up or down by k units. So (h, k) tells you where the minimum or maximum point sits, depending on whether the parabola opens upward or downward.

This pair doesn’t specify where the graph crosses the axes—that depends on solving y = 0, which involves a, h, and k together and can give zero, one, or two x-intercepts. It also isn’t describing the slope at the vertex (that slope is zero by definition for a vertex). And h and k aren’t the coefficients of the quadratic term; that role belongs to a (the coefficient of the x² term).