Each row in each table has a pair of equivalent expressions. Complete the tables. If you get stuck, try drawing a diagram.

An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters above the ground. It shoots out a drop of water at a vertical velocity of 9 meters per second.

Function models the height in meters, , of a drop of water seconds after it is shot out from the nozzle. The function is defined by the equation  .

How many seconds until the drop of water hits the ground?

1. Write an equation that we could solve to answer the question.
2. Try to solve the equation by writing the expression in factored form and using the zero product property.
3. Solve the equation by graphing the function using graphing technology. Explain how you found the solution.

1. Use the distributive property to expand . Show your reasoning, and write the resulting expression in standard form. Is it equivalent to ?
2. Study the method and make sense of what was done in each step. Make a note of your thinking and be prepared to explain it.

3. Try the method to write each of these expressions in factored form.

4. You have probably noticed that the coefficient of the squared term in all of the previous examples is a perfect square. What if that coefficient is not a perfect square?

   Here is an example of an expression whose squared term has a coefficient that is not a perfect square.

   Use the distributive property to expand . Show your reasoning and write the resulting expression in standard form. Is it equivalent to ?

5. Study the method and make sense of what was done in each step and why. Make a note of your thinking and be prepared to explain it.

6. Try the method to write each of these expressions in factored form.