Which equation choice could represent the graph shown below?
The zeroes of the polynomial are -4 and 7, which means that the bottom 2 solutions are not correct.
Now, look at the x values of the polynomial in between -4 and 7, and evaluate them at each of the 2 possible solutions. The top right one suggests that the graph is negative between -4 and 7, which is not true, so the top-left answer f(x) = (x+4)(x-7)^2 is the correct answer.
To add to what textot said....notice that the graph "cuts" the x axis at x = -4 but it " kisses" the x axis at x = 7
A graph cutiing the x axis will always have an odd multiplicity root at that point, but a graph "kissing" the x axis will have an even multiplicity root at that point
Thus......f(x) = (x + 4) ( x - 7)^2 is the only possibility