What is the value of the leading coefficient a, if the polynomial function p(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)? 2

If the polynomial function has a multiplicity of 2 at the point (−1, 0) then the factor (x-(-1))=(x+1) twice enters the polynomial representation. So, you have known one part of the left side of the polynomial function that is .

If polynomial function passes through the point (7,0), then and since you have that c=7.

At last, if polynomial function passes through the point (0,-14), then and , so a=2.
a=2.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.