What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

The vertex’s x-coordinate, 2, is the axis of symmetry. Since one x-intercept is 7, the other must be equally far from 2 on the opposite side: 2 − 5 = −3. So the function has the form f(x) = a(x − 7)(x + 3). Substituting the vertex x = 2 and y = −25 gives −25a = −25, so a = 1; therefore f(x) = (x + 3)(x − 7), choice D.

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