Describe the graph of the function f(x)=x^3+13x^2-26x+26. include the x and yintercepts and end behavior

Question

Describe the graph of the function f(x)=x^3+13x^2-26x+26. include the x and yintercepts and end behavior

Answer 1

This is positive cubic polynomial.  Therefore, f(x) approaches negative infinity as x approaches negative infinity.  f(x) infinitely increases as x infinitely increases.

 

To find the y-intercepts, evaluate f(0).

 

 

To find the x-intercepts, set f(x)=0 and solve for x.

 

x³ + 13x² - 26x + 26 = 0

 

 

Try using synthetic division to factor the left side of equation.