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I know, you've worked with
polynomials before, but we need to make sure that you really
understand how their shapes work. I definitely take an
artist's approach to these critters!
Understanding shapes and graphs will
actually help you to know what some answers in Calculus will be
before you crunch them!
I like to call the graphs of
polynomials "roller coaster graphs."
| Let's
review even degree polynomials first. Remember
that these |
| would be
polynomials whose leading term is |
 , |
 , |
 |
Starting us off is Standard
Parabola Guy. Let's really pay close attention to his basic
shape. (I'm just going to draw rough sketches here.)
 |
 |
The tails both shoot up...
We've got one valley. |
This guy touches
the x-axis once... It doesn't cross,
it just touches (a kiss). |
|
Remember that this is a multiplicity of
2 ( |
 |
) |
Continued on the
next
page
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