Lesson 9

Study “Example 3: Determining the equation of a quadratic function, given its graph” on pages 341 and 342 of the textbook. Pay particular attention to how the value for a is found.

If possible, work with a partner or small group on Try This 1. Different people could decide to use different functions.

Try This 1

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The following question will have you analyze a real-world situation and write a quadratic function that models the situation. Your function might be in the standard form, y = ax2 + bx + c, or in the vertex form, y = a(x − h)2 + k.

1. Assume that a football pass went a distance of 32 m and was 10 m higher than the passer and the receiver at its highest point. Assume the passer and the receiver are both 1.8 m tall. Sketch a parabola that shows this situation approximately to scale and label the distances you know.
   
   
2. Would you rather put the origin of the x- and y-axes at one of the ends of the trajectory, at the highest point, or at ground level? Why?
   
   
3. Choose a position for the origin and put in the x- and y-axes. Can you use the characteristics of your graph to put values in for any of the constants in y = ax2 + bx + c or y = a(x − h)2 + k?
   
   
4. Work with what you know to develop a function describing the trajectory of the football.
   
   
5. How high was the football when it is 25 m from the thrower?

Share 1

Based on your graph and development of the quadratic function in Try This 1, discuss the following questions with another student or appropriate partner.

1. Are there different functions possible to describe the same situation?
   
   
2. Can different functions still supply the same answer to the problem?
   
   
3. What assumptions did your partner make about the situation? In what ways does this differ from the assumptions you made?
   
   
4. To what extent are the assumptions reasonable?
   
   
5. How did you arrive at the quadratic function you developed?

Summarize your discussion.