f(x) = x^2. What is g(x)?

(10) points!!!

The answer to your question is the letter A. g(x) = -x² - 4

Step-by-step explanation:

From the graph, we observe that g(x) is a vertical parabola that opens downwards. So, the general formula for this parabola is:

                             (x - h)² = -4p(y - k)

For g(x)

Vertex = (0, -4)

and p must be -1/4

Then

                           (x - 0)² = -(y + 4)

Simplify

                                 x² = -y - 4

-Solve for y

                                -y = x² + 4

                                 y = -x² - 4  or g(x) = -x² - 4

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: