SOLUTION: Let f(x)=(x&#8722;8)^2(x+7)^3. Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Let f(x)=(x&#8722;8)^2(x+7)^3. Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.      Log On


   

Question 692405: Let f(x)=(x−8)^2(x+7)^3. Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x)=(x−8)^2(x+7)^3. Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.
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f(x)=(x−8)^2(x+7)^3
y-intercept:
setx=0
y=(-8)^2*(7^3)=21952
..
x-intercept
set y=0
0=(x−8)^2(x+7)^3
(x-8)^2=0
x=8 (multiplicity 2)
..
(x+7)^3=0
x=-7 (multiplicity 3)
..
number line:
<....-...-7....+.....8...+....>
f(x)>0 (-7,∞)
f(x)<0 (-∞,-7)