SOLUTION: How to do I graph this function? {{{ g(x)=(x-3)^2(x+2) }}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How to do I graph this function? {{{ g(x)=(x-3)^2(x+2) }}}      Log On


   

Question 627511: How to do I graph this function?
+g%28x%29=%28x-3%29%5E2%28x%2B2%29+
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How to do I graph this function?
%28x-3%29%5E2%28x%2B2%29
expand
x^2-6x+9(x+2)
x^3-6x^2+9x+2x^2-12x+18
x^3-4x^2-3x+18
use rational roots theorem to solve
...0...|....1......-4.......-3........18............
...1...|....1......-3.......-6........12..
...2...|....1......-2.......-7.........4..
...3...|....1......-1.......-6.........0 (3 is a root)
(x-3)(x^2-x-6)
(x-3)(x-3)(x+2)
roots are: 3 (multi. 2) and -2
y-intercept:
set equation=0
y=18
With these points, you should be able to graph given expression:
See graph below:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-20%2C+20%2C+x%5E3-4x%5E2-3x%2B18%29+