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.

one way is to plot 2 points and connect them which is what the answer choices seem to be doing

it seems to be using the y intercept and the slope

y=mx+b, m=slope, b=y-intercept (where the line hits the y axis)

slope=rise/run

y-intercept is where the line croses the y axis which is the y value where x=0

you seem to have given the wrong slope (you didn't put a number in front of te x, it should be 2/3 or 3/2 looking at the answer options)

y=? x-1

m=? because of your fault

b=-1

so it has a slope of ? and y intercept of -1, meaning it pases through (0,-1)

so draw point (0,-1) (so answer is one of the first 2 option)

if slope is 2/3, then go up 2 and right 3 then draw line through those 2 points

if slope is 3/2, then go up 3 and right 2 then draw line through those 2 points