Factored cubic graphs and their moduli

For a cubic written as three linear factors, the factors locate its zeros. Odd-multiplicity roots cross the axis; an even-multiplicity root touches. The leading coefficient determines the end behaviour. Mark all zeros and the vertical intercept. Test a value in each interval, or track sign changes at odd roots. Draw a continuous cubic with the appropriate ends. For its modulus, reflect negative portions upward and retain every zero. For (x+1)2(x-2), the zeros are -1 (touch) and 2 (cross), and the vertical intercept is -2. The negative portion to the left of 2, excluding its zero, reflects upwards. Check: the sign does not alternate at a repeated even root. A modulus graph cannot have a negative vertical intercept. Exact stationary coordinates are unnecessary unless requested.