Find a polynomial of degree n that could have the given graph. Answers may vary 

 Apr 19, 2020

The graph bounces at -6, so it has a factor of (x + 6)2.

The graph passes through -3, so it has a factor of (x + 3)

The graph bounces through 0, so it has a factor of x2.


The graph has this type of equation:  f(x)  =  a(x + 6)2(x + 3)(x2)


To see if a is positive or negative, check the end behavior:

-- if you put in a very large positive number, (x + 6)2(x + 3)(x2) will be positive (which means that the graph rises on the right-end

-- however, it drops on the right-end, so a must be negative.


Answer:  f(x)  =  -(x + 6)2(x + 3)(x2)


Now, if you have to make certain that it hits all the other points, we would have to do a lot more work ...

 Apr 20, 2020

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