Question 1208319
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Pick any three numbers at random. 
I'll select 1,4,7.


These will be the roots, aka x intercepts, of the polynomial curve.
This is where the curve either crosses the x axis or touches it.


If x = 1 is a root, then x-1 = 0, which leads to (x-1) being a factor.
The other factors are (x-4) and (x-7)


Let's say that the root at x = 7 is a double root. 
Meaning that instead of crossing the x axis, it bounces off the x axis at this point.
We'll update (x-7) to (x-7)^2


All together we have
(x-1)(x-4)(x-7)^2
I'll let the student expand this out to get a 4th degree polynomial. 


Graph of (x-1)(x-4)(x-7)^2
{{{graph(400,400,-2,10,-60,60,-1000,(x-1)(x-4)(x-7)^2)}}}
graphing window parameters are:
xMin = -2, xMax = 10
yMin = -60, yMax = 60
<a href="https://www.geogebra.org/calculator">GeoGebra</a> and <a href="https://www.desmos.com/calculator">Desmos</a> are two (of many) graphing tools you can use.
If you are most familiar with something like a TI83, then it's best to stick with it.


This isn't the only possible answer. You can pick any other values to be your roots. Also, you can scale the graph up or down. Feel free to get creative. 
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