Lesson 5

Lesson 5: Factored Form of Quadratic Functions

 

Focus

 

A field goal may be the deciding factor in a football game. The shape of the path that the football travels after it has been kicked is a parabola. The direction of the kick is important so that the ball goes between the uprights of the goal post, but the kicker must also be sure that the height of the ball will be above the horizontal crossbar of the goal post.

 

Since the football will travel the path of a parabola, you know that you can use a quadratic function to model this situation. If you consider the goal post to be the y-axis, what the kicker needs to be concerned about is the y-intercept of the parabola.

 

While the vertex form of a quadratic function allows you to quickly and easily find the vertex of the function, it is not always easy to quickly determine the x- and y-intercepts. However, you can rewrite the quadratic function in another form, called the factored form. This form is excellent for situations where the x- and y-intercepts are needed to solve a problem.

 

Lesson Questions

 

This lesson will help you answer the following inquiry questions:

• How is the graph of a quadratic function related to the constants r and s in the factored form, y = a(x − r)(x − s)?
  
  
• How do you sketch the graph of a quadratic function in the factored form?
  
  
• How do you solve problems using a quadratic function in the factored form?

Assessment

• Lesson 5 Assignment

All assessment items you encounter need to be placed in your course folder.

 

Save a copy of the Lesson 5 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.

 

 

Materials and Equipment

• graphing calculator