Exercise 11 Page 965

We are given the graph of a polynomial function with a degree of 4. Let's take a look at it by considering the points that the graph intersects the x-axis.

We want to write an equation for this graph. To do so, we will use the zeros of the graph. As we can see from the graph, our zeros lie at ( -2,0), ( 0,0), ( 1,0), and ( 3,0). By using these points we can write our equation in factored form. y= a(x-( -2)) * (x- 0) * (x- 1) * (x- 3) Since all the leading coefficients are 1 in the given options, we can set a equal to 1. We will now simplify this product. Let's begin with multiplying the first two binomials together, (x-( -2)) and (x- 0).

Next we will multiply the second pair of binomials, (x- 1) and (x- 3).

Finally, we can multiply those two expressions by distributing (x^2+2x) to every term inside the second parentheses.

Note that the equation that we found corresponds to option B.