Final answer:
To find the zeros of the given polynomial equation, we can use the Rational Root Theorem to find possible rational roots and test them. To find the y-intercept, substitute x = 0 in the equation and calculate g(0).
Step-by-step explanation:
To find the zeros of a polynomial equation, we set the equation equal to zero and solve for x. For the given equation g(x) = x^4 + 14x^3 + 32x^2 - 14x - 33, the zeros can be found by factoring or using synthetic division. However, since this is a quartic equation, it may not have easily factorable zeros. In this case, we can use the Rational Root Theorem and test possible rational roots to find the zeros.
To find the y-intercept, we set x = 0 and evaluate the function. The y-intercept is the point (0, g(0)). Simply substitute x = 0 in the equation g(x) = x^4 + 14x^3 + 32x^2 - 14x - 33 and calculate g(0).