# Graphing polynomials

#### watan

##### New member
Our goal is to create a function that gives us
The function must have:
1.π¦ β πππ‘ of β180
2. Must cross the π₯ β ππ₯ππ  exactly 4 times
3.Must be πππππππ πππ (face down)

#### Dr.Peterson

##### Elite Member
Our goal is to create a function that gives us
The function must have:
1.π¦ β πππ‘ of β180
2. Must cross the π₯ β ππ₯ππ  exactly 4 times
3.Must be πππππππ 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

##### Elite Member
Your conditions:
"2. Must cross the π₯ β ππ₯ππ  exactly 4 times"
and
"3.Must be πππππππ 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.