Graphing polynomials

[watan]

Our goal is to create a function that gives us
The function must have:
1.? − ??? of −180
2. Must cross the ? − ???? exactly 4 times
3.Must be ?????????? (face down)

 

[Dr.Peterson]

Our goal is to create a function that gives us
The function must have:
1.? − ??? of −180
2. Must cross the ? − ???? exactly 4 times
3.Must be ?????????? (face down)

What degree (minimum) must the polynomial have? What sign must the leading coefficient have?

Choose 4 arbitrary x-intercepts (preferably small numbers to keep the arithmetic simple). What does each of them tell you about the polynomial?

Find the y-intercept of your initial answer, and make adjustments to get it to -180. This may require changing one of your x-intercepts, if you didn't think ahead about that; but that will be a good learning experience.

Let's see what you've done, so we can provide any specific help you still need:

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[HallsofIvy]

Your conditions:
"2. Must cross the ? − ???? exactly 4 times"
and
"3.Must be ?????????? (face down)"
are contradictiory. If the function is decreasing (I don't know what you could mean by "face down"). If the function is always decreasing its graph can cross the x-axis only once. I thought you meant "convex downward" but then the graph could not cross the x-axis more than twice.

You titled this "Graphing Polynomials". A polynomial whose graph crosses the x-axis four times must have degree at least 4.