Question

The functions f(x) = –(x − 1)2 + 5 and g(x) = (x + 2)2 − 3 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 is a maximum for f(x) and a minimum for g(x).  This is because the squared term is never negative.

Because the larger the squared term is, the smaller f(x) is, f(x) is at MOST 5.  Similarly, because the larger the squared term is, the larger g(x) is, g(x) is at MOST -3.