Answer
One of the possible equations is
$y= x^3-5x^2+\frac{1}{4}x+15.$
Work Step by Step
One of the way is to look for the polynomial of degree $3$ with three reals zeros $x_1=-3/2, x_2=4$ and $x_3=5/2$. According to the theorem of polynomial factorization we know that this polynomial has to be of the form of
$$y=a(x-x_1)(x-x_2)(x-x_3)$$
where $a$ is nonzero real. Because we need only one function for simplicity just put $a=1$ which now yields
$$y=(x+3/2)(x-4)(x-5/2)$$
or when expanded
$$y= x^3-5x^2+\frac{1}{4}x+15.$$
