This paper investigates the excitation of quadratic quasinormal modes (QNMs) for Kerr black holes. The study focuses on the nonlinear interaction between two linear QNMs, where the amplitude of the quadratic effect is proportional to the square of the linear mode amplitude. The excitation factor, which determines the level of difficulty to excite quadratic modes, is found to depend strongly on the angular overlap between parent and child modes. For the specific case of the (l=m=2, n=0) mode, the ratio of the excitation factor is calculated as a function of the dimensionless spin parameter of the black hole, ranging up to 0.99. The results show that the ratio decreases with spin in certain scenarios, such as the channel (l=m=2, n=0) × (l=m=2, n=0) → (l=m=4), while it increases in others, like (l=m=2, n=0) × (l=m=2, n=0) → (l=5, m=4). The study also finds that the ratio does not vanish in the extremal limit. The method involves solving the frequency-domain, second-order Teukolsky equation using a semi-analytical approach, which includes reconstructing the metric through the Chrzanowski-Cohen-Kegeles method and numerically solving the equation using the shooting method along a complex contour. The results provide insights into the nonlinear dynamics of QNMs and may aid in the search for quadratic QNMs from numerical relativity and gravitational wave detections. Additionally, the study finds that the Weyl scalars can be concisely expressed in terms of the Hertz potential.This paper investigates the excitation of quadratic quasinormal modes (QNMs) for Kerr black holes. The study focuses on the nonlinear interaction between two linear QNMs, where the amplitude of the quadratic effect is proportional to the square of the linear mode amplitude. The excitation factor, which determines the level of difficulty to excite quadratic modes, is found to depend strongly on the angular overlap between parent and child modes. For the specific case of the (l=m=2, n=0) mode, the ratio of the excitation factor is calculated as a function of the dimensionless spin parameter of the black hole, ranging up to 0.99. The results show that the ratio decreases with spin in certain scenarios, such as the channel (l=m=2, n=0) × (l=m=2, n=0) → (l=m=4), while it increases in others, like (l=m=2, n=0) × (l=m=2, n=0) → (l=5, m=4). The study also finds that the ratio does not vanish in the extremal limit. The method involves solving the frequency-domain, second-order Teukolsky equation using a semi-analytical approach, which includes reconstructing the metric through the Chrzanowski-Cohen-Kegeles method and numerically solving the equation using the shooting method along a complex contour. The results provide insights into the nonlinear dynamics of QNMs and may aid in the search for quadratic QNMs from numerical relativity and gravitational wave detections. Additionally, the study finds that the Weyl scalars can be concisely expressed in terms of the Hertz potential.