The functions f (x) = (x + 1) ^2 - 2 and g (x) = - (x-2) ^2 + 1 have been rewritten using the completing-the-method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then the vertex is a minimum

• If a < 0 then the vertex is a maximum

f (x) = (x + 1) ² - 2 → has a > 0

vertex = ( - 1, - 2) and is a minimum

g (x) = - (x - 2) ² + 1 → has a < 0

vertex = (2, 1) and is a maximum