Graphing polynomials

watan

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Nov 16, 2020
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Our goal is to create a function that gives us
The function must have:
1.𝑦 βˆ’ 𝑖𝑛𝑑 of βˆ’180
2. Must cross the π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠 exactly 4 times
3.Must be π‘‘π‘’π‘π‘Ÿπ‘’π‘Žπ‘ π‘–π‘›π‘” (face down)
 

Dr.Peterson

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Nov 12, 2017
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9,567
Our goal is to create a function that gives us
The function must have:
1.𝑦 βˆ’ 𝑖𝑛𝑑 of βˆ’180
2. Must cross the π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠 exactly 4 times
3.Must be π‘‘π‘’π‘π‘Ÿπ‘’π‘Žπ‘ π‘–π‘›π‘” (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:
 

HallsofIvy

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Jan 27, 2012
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6,857
Your conditions:
"2. Must cross the π‘₯ βˆ’ π‘Žπ‘₯𝑖𝑠 exactly 4 times"
and
"3.Must be π‘‘π‘’π‘π‘Ÿπ‘’π‘Žπ‘ π‘–π‘›π‘” (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.
 
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