Explain how monetary policy can be used to prevent business cycles

There are two phases of business cycles: first, when the economy is expanding faster than the trend rate of growth, and second, when the economy is expanding slower than the trend rate of growth.
When actual growth is faster than trend growth, monetary policy may be used to try and slow it down, as it is currently unsustainable. The main method of doing this could be by raising the base interest rate. This would have the effect of increasing the cost of borrowing and increasing the incentive to save. This would cause aggregate demand to fall, as consumption will have fallen (as fewer people can now finance consumption through borrowing, as well as people being more willing to sacrifice liquidity and save, as the opportunity cost of saving is now lower). On top of this, investment will likely fall, as firms will be unable to finance as much capital as a result of the increased cost of borrowing. As AD falls, the price level will fall to a new equilibrium, causing deflationary pressure. On top of this, output will also fall, putting negative pressure on growth. This negative pressure should help reduce the actual level of growth closer to the trend level of growth.
Quantitative easing (or lack thereof) can also be used to help reduce the actual level of growth. While there isn't yet a method of monetary policy that actually takes money out of the money supply, if we assume that there already is some form of QE being used, then reducing the extent of it will reduce the rate of increase of the money supply. As the rate of increase of the money supply falls, both growth and inflation will fall, which should reduce the actual rate of growth closer to the trend rate.
If the actual rate is below the trend rate, the measures above can be used in exactly the opposite way. The only slight difference will be with QE, where one option would be able to initiate it, as opposed to just increasing the extent to which it is being used.