Question 1090850
<br>A polynomial with four zeros has degree 4 or greater.  Since you are looking for the polynomial of least possible degree that has the four give zeros, you want a polynomial of degree exactly 4.  Since it has zeros -4, -2, 0, and 2, it will be of the form<br>
{{{p(x) = a(x+4)(x+2)(x)(x-2)}}}<br>
The constant a will determine how "steep" or "flat" the graph of the function is.  In particular, it will determine the exact value of the function for any given x value.<br>
So substitute the given x value, -1, into the polynomial and determine the value of a that will produce the given y value, 3:<br>
{{{3 = a(-1+4)(-1+2)(-1)(-1-2)}}}<br>
When you have finished solving that equation to determine the value of a, you can write the complete polynomial function.<br><br>
In response to your message...<br>
Yes, a is 1/3; and yes, that is factored form. So the polynomial is<br>
{{{p(x) = (1/3)(x+4)(x+2)(x)(x-2)}}}<br>
When I graph that polynomial on my graphing calculator, it has zeros at -4, -2, 0, and 2; and it passes through (-1,3).<br>
Do you have a picture of what the graph is supposed to look like and it looks different?