Question
what three different types of fertilizers would be the best to test on plant growth?

Answer
Assuming you are going to test a flowering plant, like a Sunflower, I would guess you would grow this plant from seed, using only Peatmoss for dirt.

Make sure you have 5 pots of Sunflowers.  As I told someone else recently, you would use 5 different kinds of Fertilizing systems.

One would be high in ONLY Nitrogen.  It would not have any other nutrient in it.  Only Nitrogen.  UREA is a kind of Fertilizer with ONLY Nitrogen.  Urea is popular for Lawns.  Grass loves high Nitrogen fertilizer.

The next fertilizer would be high in Phosphorous.  The fertilizer that I know that is high in ONLY Phosphorous is called Triple Superphosphate.

Next, a fertilizer high in Potassium.  Potassium Chloride and Potassium Sulfate are loaded with it.  Potassium Chloride is used in winter to melt ice.  Its analysis is actually 0-0-60, in case your teacher wants this information.  Potassium Sulfate is a commonly used fertilizer; it also contains Sulfur, a trace mineral for plants.

The next plant would grow in a combination of all 3 of the fertilizers.

And the last Sunflower would grow with NO fertilizer.  This is known as the 'control' plant.

Let me give you a little background.

All fertilizer by law must have an 'analysis' on the container of what its nutrients are -- this is called sometimes the N-P-K analysis.  N is the Chemical symbol for Nitrogen.  P is the Chemical symbol for Phosphorous.  And K is the symbol for Potassium (also sometimes called Potash).  If you have a Periodic Table of the Elements, you will be able to find these on the chart as N, P and K.

And every container of fertilizer, somewhere on the container, will show the percentage of N, P and K.  If it says 20-20-20, it has equal parts of Nitrogen, Phosphorous, and Potassium.  If there is an analysis of 15-0-0, which is what breaks down for Sodium Nitrate, it has 15 percent Nitrogen, and Zero Phosphorous and Potassium.  If you look on a container of Miracle Gro, you will see an N-P-K number somewhere on the box that tells you the amount of each of those 3 nutrients.  All plants need those, and they need more of them than any other nutrient.  They use them up in the soil, so we add more.  Nitrogen is needed for leaves and to make Chlorophyll.  Phosphorous is needed for leaves and fruit.  And Potash is used for lots of different things.

Good luck with your project.  Thanks for writing.  Let me know if you have any questions.