Lesson 9

Lesson 9 Summary

 

In this lesson you investigated the following questions:

• How do you write a quadratic function that models a given situation and explain any assumptions made?
  
  
• How do you solve a problem, with or without technology, by analyzing a quadratic function?

You encountered a variety of situations that were modelled using quadratic functions. For many 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 readily the model provided the requested answer.

 

 

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. With the vertex form, the coordinates of the vertex tell you the values of the coefficients h and k.

 

Substituting the coordinates of the origin into a partially completed vertex form of the function, or into the standard form of the function when the origin is at the vertex, enables you to solve for the coefficient a, which will be identical in both forms of the function for that particular situation. Then you can write the complete function.

 

Refer now to the Module 3 Summary for an overview of concepts you have discovered in this module.