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)? a.f(x)=-x^2-4 b.f(x)=-(x+4)^2 c.f(x)=-(x-4)^2 d.f(x)=x^2-4

Option A - .

Step-by-step explanation:

Given : The graph of and the graph of F(x) which is changed somewhat.

To find : The equation of graph F(x)

Solution :

Since, According to the given statement we get F(x)  by doing some changes in G(x).

In the graph, it seems that F(x) is shifting vertically downward by 4 unit than G(x).

When the function is shifted to vertically downward then

i.e, f(x) → f(x)-b ⇒  f(x) shifted downward by b unit.

We also see that the graph of F(x) is reflected over x-axis.

Reflection over x-axis meas y=-x i.e, signs are changed.

So,

Therefore, Option A is correct.

The graph is .

b F(x)=-(x+4^2

Let x be the capacity of the container in gallons. Half of the container is x/2 and 2/3 of it is 2x / 3. The equation that best represent the given situation above is,
                                         x / 2   + 2   = 2x / 3
The value of x from the equation is 12. Thus, the capacity of the container is 12 gallons.