The graph of y = 2(x - 3)(x - 5)(x + 4)2 has x-intercepts 3, 5, and - 4 because they are the only possible x-values that make y = 0. This is a 4th-degree polynomial, but it has only three x-intercepts. The root x = - 4 is called a double root because the factor (x + 4) occurs twice. Make a complete graph-one that displays all of the relevant features, including local extreme values-of each of the functions in parts a-f.
a. y = 2 (x - 3)(x - 5)(x + 4)2
b. y = 2 (x - 3)2(x - 5)(x + 4)
c. y = 2 (x - 3)(x - 5)2(x + 4)
d. y =2 (x - 3)2(x - 5)(x + 4)2
e. y = 2 (x - 3)(x - 5)(x + 4)3
f. y = 2 (x - 3)(x - 5)2(x + 4)3
g. Based on your graphs from 6a-f, describe a connection between the power of a factor and what happens at that x-intercept.