Question 614920: Can someone show me how to work the following problem and graph it? I am trying to figure this out so I can use it as an example for my homework.
f(x) = (x + 6)(x + 2)(x – 4)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x) = (x + 6)(x + 2)(x – 4)
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You have x-intercepts at x = -6, x = -2, and x = 4
You have a y-intercept at f(0) = (6*2*-4) = -48
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As x goes to -oo, y goes to -oo
As x goes to +oo, y goes to +oo
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Plot a few more points and sketch the curve:
Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
The zeros of the function are clearly at -6, -2, and 4, so plot the points (-6,0), (-2,0), and (4,0). While you are at it, substitute 0 for  to find the  -intercept, namely (0,-48). Plot that point.
Note that the function zeros you plotted partition the -axis into four intervals:
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Select a value from each of the intervals and calculate the value of the function. This does two things. 1) it gives you another point to plot, and 2) it tells you whether the graph is positive or negative in that interval.
This is a 3rd degree polynomial, so you would expect, given three real zeros, one peak and one valley in the graph. Finding the exact peak and valley requires a little calculus. Write back if you want to know how to do that.
John
My calculator said it, I believe it, that settles it
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