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

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

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5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

sorry can't

step-by-step explanation:

i googled though and something came up but it was in science langueage not common english sooo