Question

The functions f(x) = (x + 1)2 − 2 and g(x) = −(x − 2)2 + 1 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

Answer:

• f(x) vertex is a minimum
• g(x) vertex is a maximum

Step-by-step explanation:

The reasoning is the same in each case: the sign of the coefficient of the squared term indicates the direction the parabola opens. If it opens upward, the vertex is a minimum; if it opens downward, the vertex is a maximum.

f(x) -- the sign of the squared term is positive, so the vertex is a minimum.

g(x) -- the sign of the squared term is negative, so the vertex is a maximum.