Question

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 maximum

Answer 1

The negative outside the parentheses indicates that the vertex is a maximum

f(x) has a minimum vertex

g(x) has a maximum

Answer 2

The vertex is the highest point in a parabola that opens down, (∩ shape) and the lowest point in a parabola that opens up (∪ shape)

f(x) has a minimum vertex

g(x) has a vertex that is a maximum

Reason:

The given functions are;

f(x) = (x + 1)² - 2

g(x) = -(x - 2)² + 1

The functions can be expanded as follows;

f(x) = (x + 1)² - 2 = x² + 2·x - 1

Given that the coefficient of x² is positive (+1), we have that the graph of the function is ∪ shaped and the function has minimum vertex

f(x) has a minimum vertex

g(x) = -(x - 2)² + 1 = -x² + 4·x - 3

The coefficient of x² is negative (-1), therefore, the graph of the function is ∩ shape and the function has a vertex that is a maximum

g(x) has a vertex that is a maximum

Learn more here;

https://brainly.com/question/9048896

https://brainly.com/question/16604682