if f(x) varies directly with x2 and f(x)=10 when x=−4 , what is the value of f(x) when x = 3?
−14.4

−5.625

5.625

14.4

Step-by-step explanation:

First thing, let's call f(x) "y".  So y varies directly with x^2 looks like this:

y = kx^2

k is our constant of variation.  We need to solve for k before we can find what we are asked to find.

Filling in:

10 = k(-4)^2 and

10 = 16 k so

k = 5/8 (reduced)

Now we will use that value of k along with the given of x = 3 to find y:

y = (5/8)(3)^2 and

y = (5/8)(9)

y = 45/8 which simplifies to

y = 5.625

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