SOLUTION: Graph the following polynomials functions and label the zeros and y-intercepts: a) f(x)=x^2(x-1)(x-5) b) f(x)=(x-3)(x^2-36)(x+2) Please I need to solve this problem!

Question 818708: Graph the following polynomials functions and label the zeros and y-intercepts:
a) f(x)=x^2(x-1)(x-5)
b) f(x)=(x-3)(x^2-36)(x+2)
Please I need to solve this problem!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I'll do problem "b":

This will be easier to do if we finish factoring. The middle factor is a difference of squares. So we can use that pattern to factor it:

For the x-intercepts we make the y equal to zero and solve for x:

Since we have a product equal to zero, one of the factors must be zero. Perhaps you can see what x values these would be. (If not, then set each factor equal to zero (x-3 = 0 or x+6 = 0 or ...) and solve.) They are:
x = 3 or x = -6 or x = 6 or x = -2
So the x-intercepts are: (3, 0), (-6, 0), (6, 0) and (-2, 0)

For the y-intercept, make the x zero:

which simplifies ...

So the y-intercept is (0, 216)

The graph might be difficult to sketch with just these intercepts. You probably want to try to build a table of values using different x-vales so you have additional points. FWIW, here's a rough sketch (with different scales on the x and y axes so you can see the most interesting parts):

The problem in part a is already fully factored. So it should be easier than part b.
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