The functions f(x) = −(x − 1)^2 + 5 and g(x) = (x + 2)^2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

a) f(x) has a maximum vertex

b) g(x) has a minimum vertex

Step-by-step explanation:

The function

has its vertex at (h,k).

If a>0, then (h,k) is a minimum vertex.

If a<0, then (h,k) is a maximum vertex.

The first function is

a=-1<0, therefore the vertex (1,5) is the maximum point.

The second function is

a=1>0, therefore the vertex (-2,-3) is a minimum point.