Lesson 5

Try This 2

Suppose the tip of the nozzle had been chosen as the point of origin in Example 1: Water Stream. The sketch would be a similar shape; however, the vertex would be at (300, 190).

1. Draw and label a graph of the problem in Example 1: Water Stream, but place the origin at the tip of the nozzle.
   
   
2. Write a quadratic function in the vertex form to model the situation. Why is the vertex form an excellent choice here?
   
   
3. Calculate the value of the coefficient a by substituting a known point that lies on the function.
   
   
4. What is the height of the stream of water when it is a horizontal distance of 70 cm from the nozzle? Compare your answer to the answer found in Example 1: Water Stream. The answers should be the same. Which method do you prefer?

Save your responses in your course folder.

Placing the Origin

When modelling a problem, you choose a position for the origin that allows you to make a quadratic equation with a minimum number of computations. Putting the origin at the vertex, a point under the vertex, or at one of the endpoints of the parabola usually works best.

No matter where you place the origin or whether you use the standard form or vertex form to develop the quadratic equation, the final solution should be the same.