Yis directly proportional to the square of x
y=96 when x = 4

Find a formula for y in terms of x

Step-by-step explanation:

y being directly proportional to the square of x means that the ratio between the two will always be equal to some constant (let's call it k). In equation form, we'd say:

We're told that y = 96 when x = 4, so we can plug those values in to find k:

Our more general equation is now

If we want to put y in terms of x, we need to get the y by itself on one side of the equation, which we can do here by multiplying both sides by x², giving us