Polynomial Functions: graphing x^4 - 2, -x^3 - 3x^2, -x^3 +

wind

Junior Member
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Sep 20, 2006
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graph each of the functions

e) f(x)= x^4 - 2
f) f(x)= -x^3 - 3x^2

how do I factor these to find the roots? I tryed using the factor thm for thw first one but it did not work...and the root of 2 is not a whole number. Can someone please tell me how to do this, thanks.

g) y=-x^3 + 3x^2 - x
= -x ( x^2 + 3x)

so the roots are 0 and nedative 3 but since the X^2 is in the brackets and that can't be further simplified in to whole numbers, does'nt that mean that -3 is a turning point, since it is a double root? So why does the graph do down after passing the -3 pt?
 
What didn't work?

\(\displaystyle \L\,x^{4} - 2 = (x^{2}+\sqrt{2})(x^{2}-\sqrt{2}) = (x^{2}+\sqrt{2})(x+\sqrt[4]{2})(x-\sqrt[4]{2})\)

\(\displaystyle \L\,-x^{3} - 3*x^{2} = -x^{2}*(x-3)\)

Anyway, your problem statement say sto graph them. Roots are not mandatory. Start with the y-intercept, maybe. Plot a few points.
 
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