Which statement describes the graph of f(x) = –4x3 – 28x2 – 32x + 64?
a. the graph crosses the x axis at x = 4 and touches the x axis at x = –1.
b. the graph touches the x axis at x = 4 and crosses the x axis at x = –1.
c. the graph crosses the x axis at x = –4 and touches the x axis at x = 1.
d. the graph touches the x axis at x = –4 and crosses the x axis at x = 1.

the answer is D

Step-by-step explanation:

D. The graph touches the x axis at x = –4 and crosses the x axis at x = 1.

Step-by-step explanation:

You are given the function

1. Factor this function:

2. This function is equal to 0 at

The degree at factors are:

since 2 is the even number, the graph touches the x-axis at x=-4.

since 1 is the odd number, the graph crosses the x-axis at x=1.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)