Question 916554
f(x) = 12x^3 - 12x^2 - 24x 
 f(x) = 12x(x^2 - x - 2) 
 f(x) = 12x(x+1)(x-2) 
 x-int:(0,0)(-1,0)(2,0) 
 y-int:(0,0) 
good Work.
What goes Up, in this case, must go down and visa-versa
Where does it turn: f' = 0 gives us that: at x =  -.55, 1.22  (rounded)
f(-.55) = 7.57, f(1.22) = -25.35 (rounded)
Regardless...for sketching using the visual of ~ -.5  and ~1 will do.
f(-.5) = 7.5, f(1) = -24
{{{drawing(300,300,   -6, 6, -30, 30, grid(1), 
circle(2,0,0.2),
circle(-1,0,0.2),
circle(1.22,-25.35,0.2),
circle(-.55,7.57,0.2),
graph( 300, 300, -6, 6, -30, 30,0, 12x^3 - 12x^2 - 24x) )}}}