Question

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.

Answer 1

see explanation

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