A quadratic function g(x) passes through the points (-8, 33), (2, 1), and (8, 1).

Question

Which statement correctly describes g(x)?

A. The line x = -5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.

B. The line x = -5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.

C. The line x = 5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.

D. The line x = 5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.

Answer 1

Plotting the points we have:

We can see that the line of symmetry is halfway between x = 2 and x = 8 making it at x = 5.

We can see that the graph, a parabola, must have a minimum value at x = 5 in order to go through (-8, 33)