Question

The functions f(x) = - (x + 4) ^ 2 + 2 and g(x) = (x - 2) ^ 2 - 2 have been rewritten using the completingthe-square methodApply 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

Answer 1

Answer:

The vertex for f(x) = -(x + 4)² + 2 is a maximum

The vertex for g(x) = (x - 2)² - 2 is a minimum

Step-by-step explanation:

The vertex form of the equation of a parabola is given as:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola

If a > 0, the vertex of the parabola is a minimum

If a < 0, the vertex of the parabola is a maximum

The given functions are:

f(x) = -(x + 4)² + 2

g(x) = (x - 2)² - 2

Comparing f(x) = -(x + 4)² + 2 with y = a(x - h)² + k

a = -1

Since a < 0, the vertex of the function f(x) = -(x + 4)² + 2 is a maximum point

Comparing g(x) = (x - 2)² - 2 with y = a(x - h)² + k

a = 1

Since a > 0, the vertex of the function g(x) = (x - 2)² - 2 is a minimum point.