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One of the things that causes cut flowers to wilt so quickly is bacteria in the water. The most basic thing you can do to preserve cut flowers is to change the water once a day. Use cold water and add ice cubes before adding the flowers to the vase. You can also treat the water to inhibit bacterial growth. Two tablespoons of sugar, apple cider vinegar, or even a penny at the bottom of the vase can keep your flowers looking fresh for longer. A small amount of bleach in your vase water works well to control bacteria growth mentioned before and keep water clear. Different types of flowers have different types of stems, and different types of stems require different treatments in order to keep your flowers looking fresh. The most basic way to treat the stems is to trim the ends a small amount each day when you change the water and cut them at a 45° angle but you may also want to:  Split the bottom inch of the stem for woody stems like lilacs. This helps it absorb more water. Sear the stems of milky stemmed flowers like poinsettias. This milk harms other flowers in the bouquet. Daffodils also produce this milk but searing won't work for them, so avoid using them in mixed bouquets. Fill the stems of hallowed stem flowers, like dahlias. Fill the stem with water, plug the hole with your finger, and then submerge them. This will help them stay upright and fresh. If it's too hot or too cold in the spot you've placed your cut flowers, they will wilt much more quickly. Move them to a good, temperature neutral spot. Some flowers, however, do better at warmer temperatures. If you have tropical flowers, like Bird of Paradise, consider a warmer spot. Remove leaves, flowers, or branches which would fall below the water line. Having these in the water encourages bacteria growth. Once flowers start to get really wilted, pinch them off. This will help keep the plant from throwing a bunch of energy into maintaining them. Don't use household scissors to cut plants. These are intended for paper and can hurt the plant's ability to absorb water. Use tools that are intended for flowers and plants and make sure they're kept sharp. You can also add preservatives to the water, like Floral Life, and these will help provide your flowers with the nutrients that they miss out on after they're cut. This will significantly increase the life of your cut flowers.
Change the water regularly. Treat the water. Take care of the stems. Keep an eye on the temperature. Remove excess leaves. Cull flowers as necessary. Use appropriate tools. Use preservatives.