Lesson 5

Discover

 

You will analyze a real-world situation and model the situation by writing a quadratic function in the standard form, y = ax2 + bx + c , or in the vertex form, y = a(x − p)2 + q.

 

Try This 1

 

iStockphoto/Thinkstock

 

Assume that the football pass in the picture went a distance of 32 m and was 10 m higher than the thrower and the receiver at its highest point. Assume that both the thrower and the receiver are 1.8 m tall.

1. Sketch a parabola that shows this situation approximately to scale, and label the distances you know.
   
   
2. Would you rather put the origin, (0, 0), at one of the endpoints of the trajectory, at the height of the thrower or receiver, at the highest point of the throw, or at ground level? Explain your choice.
   
   
3. Choose a position for the origin and put in the x- and y-axes. Use the characteristics of your graph to find values to replace any of the parameters a, b, c, p, or q in y = ax2 + bx + c or in y = a(x − p)2 + q.
   
   
4. Use a known point to help solve for other parameters and develop a function describing the trajectory of the football.
   
   
5. How high is the football when it is 25 m from the thrower?

Save your responses in your course folder.

 

Share 1

 

Share your answers to Try This 1 with a partner or group, and then discuss the following questions.

1. What help can you give your group or partner to help everyone develop a function to describe the pass?
   
   
2. Are there different functions possible to describe this situation? Will each function supply the same answer to the problem?
   
   
3. What were the differences and similarities between the assumptions each person had to make about the situation?

Save your responses in your course folder.