Question

What of the functions is represented by the graph?

On a coordinate plane, a parabola opens downward. It goes through (negative 4, negative 4), has a vertex at (0, 4) and goes through (4, negative 4).

Answer 1

The parabola is symmetric about the y-axis and has vertex (0,4), so it has form y = ax^2 + 4. Use (4, −4):

−4 = a(4^2) + 4 → −4 = 16a + 4 → 16a = −8 → a = −1/2.

Thus the function is y = −(1/2)x^2 + 4 (equivalently y = 4 − (1/2)x^2).