Question

The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

Answer 1

The vertex for the first equation is a maximum because it undergoes a reflection across the x-axis, so the parabola opens in the opposite direction.

The vertex for the second equation is a minimum because the parabola opens upward.