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Polynomials

So, what would this guy look like?

f( x ) = -x^4 + some x stuff ... the - means it's up-side-down








Both tails shoot down...		roller coaster graph with one valley and two mountains

 

I'm not really sure about those wobbles though...  Not without the specific info...  And not without a graphing calculator...  OR CALCULUS!  So, I'll just do my best and draw a basic shape for now.

Remember that a 4th degree polynomial can cross the x-axis, at most, FOUR times.  This info really helps with these rough sketches!roller coaster graph with one valley and two mountains ... crosses the x-axis four times

 

What aboutf( x ) = x^6 + some x stuff?

It can cross, at most, six times...  positive even degree always starts with the left tail up...  Let this info guide the shape as you draw...

roller coaster graph with three valleys and two mountains 

Both tails shoot up.


It COULD have two mountains and three valleys.