A polynomial with zeroes at -1 and 1 is a multiple of
[tex](x-1)(x+1) = x^2-1[/tex]
So, your polynomial is something like
[tex]a(x^2-1)[/tex]
We can determine the value of a by imposing the passage through (0,-6):
[tex]f(0) = a(0-1)=-a=-6 \iff a=6[/tex]
So, the function is
[tex]6(x^2-1)[/tex]
