Getting started -- Your plant was grown in filtered light, not direct sun, so it should be started in filtered sun or shade, and slowly moved into more light over a period of a few weeks. This will give your plant time to adjust to sun without burning or wilting.
Pot size -- I recommend starting your plant in a 1 to 5 gallon (4 to 20 liter) pot with potting soil, even if you plan on putting it into the ground later.
Soil -- The tree likes well-draining, slightly-acid soil. A good soil mix is 2 parts potting soil to 1 part perlite. An alternative is well-decomposed compost and perlite in equal parts.
Planting out -- Once your plant has grown a foot taller, you may plant in the ground (avoid heavy clay soils). If you're going to keep it in a container, repot to a 10-15 gallon (20-60 liter) pot whenever the roots reach the bottom of the container. Repot again to a larger pot as needed. The size of the final pot depends on how big you let the plant grow.
Repot gently to avoid breaking apart the soil ball, which can damage the roots. To help keep the soil ball together, water the soil first. For the first week after repotting, give no fertilizer or prolonged sun.
Climate -- This Dogwood prefers part sun, except in cooler climates, where it can take full sun. It does not need a lot of direct sun to be happy. In hot areas, it's best to give it some afternoon shade. Avoid placing it where heat can collect, like near a sunny wall.
The tree is said to be hardy in Zones 6, but i recommend protecting the plant from frost the 2-3 years. In cold-winter areas, i would give it overhead protection, such as under a tree, to provide some frost protection. Or just grow it in a pot and bring it indoors over the winter. When the plant nears flowering size, it might need cooler nights in winter (below 55-60°F / 12-16°C) to encourage flowering, although i am not certain about this.
Over about 40% humidity is recommended.
Watering -- Aim to keep the soil evenly moist (but not soggy) most of the time. Don't let the soil dry out completely. You can check the soil moisture using a moisture meter probe, which are sold at most garden shops inexpensively.
Fertilizing -- Feed about every 2-3 months during the growing season with a slow-release (pelleted or organic) fertilizer.
Pruning -- Pruning is optional. If you want it to have a short, bushy shape, pinch off the growing tip of the tallest stem, and this will encourage side branches to form. If you prefer a tall, tree-like shape, remove the lower branches.
Bugs to watch for -- This will vary in different parts of the country. Dogwood borer might be a problem in prone areas. Indoors, watch for typical indoor pests like spider mites (tiny "dots" under the leaves, with webbing), mealy bugs, thrips, and scale (brown discs on the stem - hard to see).
If you have any questions, feel free to email me.
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