SOLUTION: Find the following for the function f(x)=(x+4)^2(x-2)^2. 1.)Find the x- and y-intercepts of the polynomial function f 2.)Find the power function of the graph of f resembles for

Algebra ->  Rational-functions -> SOLUTION: Find the following for the function f(x)=(x+4)^2(x-2)^2. 1.)Find the x- and y-intercepts of the polynomial function f 2.)Find the power function of the graph of f resembles for      Log On


   

Question 1002493: Find the following for the function f(x)=(x+4)^2(x-2)^2.
1.)Find the x- and y-intercepts of the polynomial function f
2.)Find the power function of the graph of f resembles for large values of x
3.)Determine the maximum number of the turning points on graph f
4.)Determine the behavior of the graph of f near each x-intercept
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%2B4%29%5E2%28x-2%29%5E2
f%28x%29=%28x%5E2%2B8x%2B16%29%28x%5E2-4x%2B4%29

f%28x%29=x%5E4-4x%5E3%2B4x%5E2%2B+8x%5E3-32x%5E2%2B32x+%2B16x%5E2-64x%2B64
f%28x%29=x%5E4%2B4x%5E3-12x%5E2-32x%2B64

1.)Find the x- and y-intercepts of the polynomial function f
0=%28x%2B4%29%5E2%28x-2%29%5E2
x-intercepts:
if 0=%28x%2B4%29%5E2=>x=-4 (multiplicity 2)
if 0=%28x-2%29%5E2=>x=2 (multiplicity 2)
y-intercept
y=%280%2B4%29%5E2%280-2%29%5E2
y=%284%29%5E2%28-2%29%5E2
y=%2816%29%284%29
y=64

2.)Find the power function of the graph of f resembles for large values of x
The function resembles y+=+x%5E4.
3.)Determine the maximum number of the turning points on graph f
three turning points
4.)Determine the behavior of the graph of f near each x-intercept
near x-intercepts x=-4 and x=2:
the graph of f bounces off the axis at the root

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+85%2C+%28x%2B4%29%5E2+%28x-2%29%5E2%29+