SOLUTION: The graph of (x)=-(x+3)^2(x-5)^3 has x-intercepts at x=-3 and x=5. At and immediately surrounding the point x=-3, the graph resembles the graph of what function? Choose one.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The graph of (x)=-(x+3)^2(x-5)^3 has x-intercepts at x=-3 and x=5. At and immediately surrounding the point x=-3, the graph resembles the graph of what function? Choose one.       Log On


   



Question 1024726: The graph of (x)=-(x+3)^2(x-5)^3 has x-intercepts at x=-3 and x=5.
At and immediately surrounding the point x=-3, the graph resembles the graph of what function?
Choose one.
A. y=x
B. y=x^2
C. y=x^3

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the root x=+-3 is repeated twice, so it has a multiplicity of 2
the root x=+5 is repeated three times, so it has a multiplicity of 3
multiplicity of 2 means the function will behave like x%5E2 near the root x+=+-3
and multiplicity of 3 means the function will behave like x%5E3 near the root x+=+5
so, your answer is B. y=x%5E2