SOLUTION: I need help with this problem! Thank you! Find the following f(x)=(x+5)^2(x-2)^2 ​(a) Find the​ x- and​ y-intercepts of the polynomial function f. &#820

Algebra ->  Rational-functions -> SOLUTION: I need help with this problem! Thank you! Find the following f(x)=(x+5)^2(x-2)^2 ​(a) Find the​ x- and​ y-intercepts of the polynomial function f. &#820      Log On


   



Question 1044942: I need help with this problem! Thank you!
Find the following f(x)=(x+5)^2(x-2)^2
​(a) Find the​ x- and​ y-intercepts of the polynomial function f.
​(b) Determine whether the graph of f crosses or touches the​ x-axis at each​ x-intercept.
​(c) Put all the information together to obtain the graph of f.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = (x+5)^2 * (x-2)^2
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when x = 0, f(x) is the y intercept
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f(x) = 5^2 * (-2)^2 = 100
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when f(x) = 0 we have an x intercept
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we have 2 x-intercepts, x = -5, x = 2
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here is the graph
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+graph%28+300%2C+200%2C+-8%2C+5%2C+0%2C+400%2C+%28x%2B5%29%5E2++%2A+%28x-2%29%5E2%29+
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a) y intercept is 100, x intercepts are -5 and 2
b) f(x) touches the x axis at (-5,0) and (2,0) since f(x) is always > or = 0
c) see graph above
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