Answer:
[tex]y=6x^2[/tex]
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:
[tex]\dfrac{y}{x^2}=k[/tex]
We're told that y = 96 when x = 4, so we can plug those values in to find k:
[tex]\dfrac{96}{4^2}=\dfrac{96}{16}=6=k[/tex]
Our more general equation is now
[tex]\dfrac{y}{x^2}=6[/tex]
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
[tex]y=6x^2[/tex]
