Write the function in standard form: (f(x)=ax^3+bx^2+cx+d)
Find the y-intercept by evaluating (f(0))
Find the x-intercepts by solving (f(x)=0)
Determine the end behavior from the sign of (a)
Find the turning points by solving (f'(x)=0)
Use the second derivative or test intervals to classify turning points
Find the inflection point by solving (f”(x)=0)
Plot the intercepts, turning points, and inflection point
Evaluate additional points on both sides of the graph
Sketch a smooth curve through the points
Check that the graph matches the end behavior and overall cubic shape