Thanks for contacting "ask extension" about fertilizer requirements for tomato plants:
Tomatoes respond well to fertilizer applications, particularly phosphorus. A complete fertilizer contains nitrogen (N), phosphorus (P), and potassium (K) (along with other nutrients). A fertilizer’s content specifies these nutrients in this order: N-P-K. 
To give the young plants a good start, place a handful (1 to 2 ounces) of a complete fertilizer (4-12-4, 5-10-5, or 5-10-10) in a circle 3 inches away from the plant and 3 to 4 inches deep. An additional application of nitrogen about fruit set time, placed in a circle 1 foot away from the plant, helps sustain production. More applications of nitrogen fertilizer are not recommended, as it tends to promote excessive vine growth and delay fruit maturation.

Note: Plants can use chemical fertilizers as soon as they are applied. Soil bacteria and fungi must act on most organic nutrient sources to change them into a usable form. Thus, if you use mostly organic fertilizers, you may need to add a small amount of a source of more readily available nitrogen early in the season to ensure adequate plant nutrition until the organic sources become available to plants. Options include liquid fish, blood meal and chemical fertilizer.
Let me know if you have further questions.
Happy gardening!