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Question 79143: Graph the following polynomials by using the zero product property and end behavior.
y= -(x+5)(x-3)(x-6)
y= (x+4)^2(x-1)(x-3)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! y= -(x+5)(x-3)(x-6)
The zeroes are x=-5, x=3, x=6
Mark those points on the x-axis.
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If you were to multiply out the right side the highest power term
would be -x^3 and the y=intercept would be at -5*-3*-6=-90
Therefore as x gets larger y gets very negative
So off toward the right of x=6 sketch the curve going down
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Also as x gets more and more negative y gets very positive
So off to the left of x=--5 sketch the curve coming down to the
x-axis from above.
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So, from left to right:
The curve comes down to x=-5
It crosses the x-axis at x=-5
It crosses the y-axis at -90
it crosses the x axis at x=3
It turns around and crosses the x-axis at x=6
It gets more and more negative as x gets more and more positive.
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Cheers,
Stan H.
y= (x+4)^2(x-1)(x-3)
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