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

Guest Apr 19, 2020

#1**+1 **

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 x^{2}.

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

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)(x^{2}) 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)(x^{2})

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

geno3141 Apr 20, 2020