Lesson 5

Lesson 5 Summary

 

In this lesson you investigated the following questions:

• How are quadratic functions developed and used to model real-life situations?
  
  
• What assumptions are appropriate to model a situation using quadratic functions?

You encountered a variety of situations that you modelled by developing quadratic functions. For many of the situations, including parabolic trajectories and parabolic structures, drawing a sketch of the situation and putting in axes helped to write the quadratic function.

 

You learned that the axes could be placed at various positions on the sketch. Some of the more useful positions were at the vertex, directly under the vertex, and at either end of the parabolic path. The position chosen for the vertex influenced how easily a solution could be found.

 

To write a quadratic function from a sketch of the graph, the coordinates of the vertex and at least one other point on the graph should be known. Then you can write the complete function.

 

You expanded your skill in using a graphing calculator. You used a graphing calculator to refine your estimates of the maximum, minimum, and intercept points of a function.

 

In the next module you will investigate how to factor and solve quadratic equations that, in this lesson, you could only estimate using a graphing calculator. You will also learn to solve quadratic inequalities.