From the zeros you can write out a factored version of your polynomial. There are multiple correct answers here. One factored form of your polynomial might be:
f(x) = ax(x + 4)(x - 2)(x - 1) where "a" is a constant.
I got this from the factor theorem, which states: The binomial (x - a) is a factor of the polynomial f(x) if and only if f(a) = 0. In other words, if "a" is a zero, then (x - a) is a factor of your polynomial. Note that for the zero of 0 in your problem, that factor works out to (x - 0) or just x. If your problem had included a factor "k" times, then you would have had the factor (x - a)k in your polynomial equation.
We now have to adjust our equation for f(x) so that it passes through the given point. This will done by determining a value for the coefficient "a".
Note: f(1/2) = 1.6875a
Setting this equal to 27, we see that "a" must be 16.
