SOLUTION: Draw the graphs of each of the following on the coordinate axes below: f(x) = 12x^3 - 12x^2 - 24x f(x) = (1/64)(x-3)^2(x+4)^3 Please explain in detail how I would figu

Algebra ->  Graphs -> SOLUTION: Draw the graphs of each of the following on the coordinate axes below: f(x) = 12x^3 - 12x^2 - 24x f(x) = (1/64)(x-3)^2(x+4)^3 Please explain in detail how I would figu      Log On


   

Question 916126: Draw the graphs of each of the following on the coordinate axes below:

f(x) = 12x^3 - 12x^2 - 24x
f(x) = (1/64)(x-3)^2(x+4)^3

Please explain in detail how I would figure these out/set them up. I am so lost right now I don't know where to start....
Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+12x%5E3+-+12x%5E2+-+24x+
choose several values for x, calculate f%28x%29 to get ordered pairs:
x=0
f%280%29+=+12%2A0%5E3+-+12%2A0%5E2+-+24%2A0=0+
x=1
f%281%29+=+12%2A1%5E3+-+12%2A1%5E2+-+24%2A1=12-12-24=-24
x=-1
f%28-1%29+=+12%2A%28-1%29%5E3+-+12%2A%28-1%29%5E2+-+24%2A%28-1%29=-12-12%2B24=0

x=2
f%282%29+=+12%2A2%5E3+-+12%2A2%5E2+-+24%2A2=12%2A8-12%2A4-24%2A2=96-48-48=96-96=0
x=-2


x=4
f%284%29+=+12%2A4%5E3+-+12%2A4%5E2+-+24%2A4=12%2A64-12%2A16-24%2A4=768-192-96=480
x=-4

so, you got points: (0,0), (1,-24),(-1,0),(2,0),(-2,-96),(4,480,(-4,-864)
plot them and draw a line through:


I believe you can do same with f%28x%29+=+%281%2F64%29%28x-3%29%5E2%28x%2B4%29%5E3.