Lesson 6

Modelling a Problem with a System of Two Quadratic Equations

 

Try This 5

 

Launch Modelling Quadratic-Quadratic Equations: Animated Fountain. Work through the example to model and solve a problem based on a system of quadratic-quadratic equations. You will be given a lot of support to model the problem. Once you have the system set up, you will have the opportunity to solve the system independently based on the strategies you have learned in this lesson. Then complete the following question. Note: You will copy your answer to this question into your Lesson 6 Assignment later in the lesson.

In an animated fountain, a stream of water is shot to a maximum height of 10 ft and re-enters the fountain 6 ft away. A second stream of water is shot to a maximum height of 5 ft but re-enters the fountain 14 ft away. Each stream follows a parabolic path. At what horizontal distance from the water jets are the two streams at the same height?

 

Copy the system that you modelled in Modelling Quadratic-Quadratic Equations: Animated Fountain as part of your solution. Solve the system algebraically showing all of your work. You do not need to show how you obtained the equations.

 

Save your work in your course folder.

 

Self-Check 3