Answer:
Step-by-step explanation:
The standard, factored polynomial function is given by:
Where <em>a</em> is the leading coefficient,
<em>p</em> and <em>q</em> are factors,
And <em>n </em>and <em>m</em> are the powers or multiplicity they are being raised to.
We know that our polynomial function is of degree 4.
We have a root of multiplicity of 2 at x=-2.
So, our factor is:
It is has a multiplicity of 2, it is squared. So:
We have another root with multiplicity of 1 at x=6.
So, our factor is:
And since it is to the first power, we can write it as is.
Finally, we have another root of multiplicity of 1 at x=2.
So, our factor is:
Therefore, our entire function is:
We still have to determine our leading coefficient, <em>a</em>.
We can use that y-intercept. The y-intercept is at (0, 10). So, when x=0, y=10. By substitution:
Evaluate:
Multiply:
Therefore:
Therefore, our final function is: