The graph of f(x), shown below, resembles the graph of g(x)=x^2, but it has been changed somewhat. which of the following could be the equation of f(x)?

The equation of the resulting function F(x) is:

Hence, option: B is correct.

Step-by-step explanation:

We are given a graph of the function G(x) as:

We are asked to find what could be the possible representation of the function F(x).

We know that the graph of function F(x) is a horizontal stretch of the function G(x).

This means that the factor that is multiplied to G(x) is 'k'

where 0< k <1.

Also the graph is shifted 3 units vertically down hence the graph of the resulting function F(x) is:

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