Sketch the graph. Label all vertices and intercepts. y=x^3-3x^2-x+3

Question

please show work for how to get the vertices and intercepts 

Answer 1

Factor by grouping.

 

y = x²(x - 3) - (x - 3)

 

y = (x - 3)(x² - 1)

 

y = (x - 3)(x - 1)(x + 1)

 

The zeros are x=-1 , x=1, and x=3.

 

A maximum value occurs in between x=-1 and x=1. A minimum value occurs in between x=1 and x=3.

 

 

Plot the x-intercepts, the two local extremas (maximum and minimum).  You should know the y-intercept.