QM Q2.) Determine whether the graph crosses the​ x-axis, or touches the​ x-axis and turns around at each​ x-intercept. 

• Asdfjkadfjkakjf:

  by plotting y=x^3+8x^2-4x-32, the zeros are at x=-8, -2 and 2

  at all three zeros, it crosses the x-axis. theres no touch n turn around.

  see attached plot

  
  

• nustopocru: f(x)=x^3+8x^2-4x-32
  note that f(2)=0 so x=2 is one of the zero
  dividing f(x) by (x-2)
  the quotient is x^2+10x+16 which factors into (x+2)(x+8)
  combining f(x)=(x-2)(x+2)(x+8)
  the zeros are -8, -2 and 2
  
  for f(x) to "turn around", it must be a max or min
  f'(x)=3x^2+16x-4=0
  
  at greatest zero, f'(2)<>0 so it crosses the x-axis
  
  at second greatest zero, f'(-2)<>0 so it crosses the x-axis
  
  at smallest zero, f'(-8)<>0 so it crosses the x-axis