Evaluating f(0), a very important property exists: the multiplication property of 0. This property states that a•0=0; any number multiplied by zero is always 0.
So, let’s evaluate:
f(0)=-(0)^3+7(0)^2-2(0)+12
All the terms with the variable x are accompanied by a coefficient and exponents, which both, by definition, are forms of multiplication. So, we know that a•0=0, so any term with 0 is canceled to 0. We get:
f(0)=0+12
f(0)=12