SOLUTION: find the following for the function f(x)=(x+4)^2(x-2)^2 a. find the x and y intercepts b.determine whether the graph of f crosses or touches the x-axis at each untercept c.put a

Algebra ->  Rational-functions -> SOLUTION: find the following for the function f(x)=(x+4)^2(x-2)^2 a. find the x and y intercepts b.determine whether the graph of f crosses or touches the x-axis at each untercept c.put a      Log On


   

Question 865756: find the following for the function f(x)=(x+4)^2(x-2)^2
a. find the x and y intercepts
b.determine whether the graph of f crosses or touches the x-axis at each untercept
c.put all the information together to obtain graph of f
thanks in advance for the help
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%2B4%29%5E2%28x-2%29%5E2

This is already in factored form. x intercepts are -4 and +2.
y-intercept happens for highlight%28f%280%29%29=4%5E2%2A2%5E2=16%2A4=highlight%2864%29.

Examine the function factors very carefully. Each individual binomial factor may be less than, equal to, or greater than zero; but because both factors are squared, f(x) stays POSITIVE, so will always be at or above the horizontal axis. This means, f(x) NEVER crosses the x axis at any x intercept.

The vertical labeling is imprecise, but here is a fair representation of the graph:
graph%28400%2C400%2C-7%2C5%2C-5%2C80%2C%28x%2B4%29%5E2%28x-2%29%5E2%29