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. (10 points)

The vertex for  would represent a minimum because the coefficient of the binomial (x+1) squared term is positive (understood to be in front of the parenthesis). Think about the Vertex Form:  where "" is the coefficient of the binomial and (h, k) is the vertex. If "" is positive the parabola opens up ∪ (making the vertex the lowest point of the graph).  If "" is negative the parabola opens down ∩  (making the vertex the highest point of the graph).
Therefore:
The vertex of f(x) is a MINIMUM because .
The vertex of g(x) is a MAXIMUM because