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When a hybrid car is being driven, the different subsystems—gas engine, electric motor, generator, and regenerative brakes—are not always in operation at any given moment. Depending on the driving conditions, the engine might be off and the brakes might be regenerating the battery, for example. 
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When the car is stopped and then starts up slowly, the low power requirements can be met by the electric motor alone. In this mode, the gas engine is off, and the car runs highly efficiently off the batteries. The car also runs on the motor alone when cruising at moderate speeds, such as under 40 mph.
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If the driver presses the accelerator pedal down a lot to accelerate rapidly, more power is needed than can be delivered by the motor alone. In rapidly accelerating operation, the engine and motor both are running to provide maximum power. The battery’s charge is being used to power the motor.
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When driving at highway speeds, the car needs enough power to overcome substantial air resistance. The engine is on, but often it delivers more energy than needed just to move the car forward. In this operational mode, the excess power from the gas engine powers the electric generator, thereby recharging the battery.
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If the driver sees a slowdown in traffic—or a red traffic light—far ahead, she may switch to coasting mode. The gas engine turns off and the electric motor is not needed, so no energy is expended. This is equivalent to putting a standard car’s engine into neutral, except that the hybrid car’s gas engine has shut off temporarily to save energy!
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If the driver wants to slow down somewhat more rapidly, she releases the accelerator pedal altogether and the regenerative braking system turns on. The car now slows down, because the car’s kinetic energy is being transformed into electrical energy for storage in the battery. The engine and motor are both turned off, so no energy is consumed.
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If the driver needs to brake more rapidly, she presses the brake pedal. In this mode, both the standard brakes and the regenerative braking systems are in operation. Once again, the engine and motor are both turned off, so no energy is consumed.
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In which operating modes is the gasoline engine turned off?
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The gasoline engine is turned off when the car is accelerating slowly, cruising at slower speeds (i.e., not highway speeds), coasting, and braking.
Note that these operating modes are the times when the car is most efficient, because no gasoline is being used. These are the operating modes in which a hybrid car really shines over a standard car! 
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