Question

Tempestt graphs a function that has a maximum located at (–4, 2). Which could be her graph?

On a coordinate plane, a parabola opens up. It goes through (negative 6, 6), has a vertex at (negative 4, 2), and goes through (negative 2, 6).
On a coordinate plane, a parabola opens up. It goes through (2, 6), has a vertex at (4, 2), and goes through (6, 6).
On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 2), has a vertex at (negative 4, 2), and goes through (negative 2, negative 2).
On a coordinate plane, a parabola opens down. It goes through (2, negative 2), has a vertex at (4, 2), and goes through (6, negative 2).

Answer 1

The third graph.

A maximum at (−4, 2) means the vertex is (−4,2) and the parabola must open down. The third option has vertex (−4,2), opens down, and the symmetric points (−6, −2) and (−2, −2) lie below the vertex, so it fits.