Analyze the function’s graph to determine which statement is true. Over the interval [–2.5, 0.5], the local maximum is 2.
As the x-values go to positive infinity, the function’s values go to negative infinity.
The function is decreasing over the interval (–1, 0.75).
The function is negative for the interval [–2, 0].

A. Over the interval [–2.5, 0.5], the local maximum is 2.

Step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15