Building Quadratic Functions to Describe Situations (Part 2)

5 min

Narrative

In this Warm-Up, students consider what happens if an object is launched up into the air but is unaffected by gravity. The work here reminds students that an object that travels at a constant speed can be described with a linear function. It also familiarizes students with a projectile context used in the next activity, in which students will investigate a quadratic function that more realistically models the movement of a projectile with gravity in play.

Students who use a spreadsheet to complete the table practice choosing tools strategically (MP5).

Launch

Ask a student to read the opening paragraph of the activity aloud. To help students visualize the situation described, consider sketching a picture of a person with a t-shirt launcher pointing straight up, 5 feet above ground. Ask students to consider what a speed of 90 feet per second means in more concrete terms. How fast is that?

Students may be more familiar with miles per hour. Tell students that the speed of 90 feet per second is about 61 miles per hour.

Consider arranging students in groups of 2 so they can divide up the calculations needed to complete the table. Provide access to calculators, if requested.

Student Task

A person with a t-shirt launcher is standing in the center of the field at a soccer stadium. He is holding the launcher so that the mouth of the launcher, where the t-shirts exit the launcher, is 5 feet above the ground. The launcher sends a t-shirt straight up with a velocity of 90 feet per second.

Imagine that there is no gravity and that the t-shirt continues to travel upward with the same velocity.

  1. Complete the table with the heights of the t-shirt at different times.
    seconds 0 1 2 3 4 5 tt
    distance above ground (feet) 5                                                                                          
  2. Write an equation to model the distance in feet, dd, of the t-shirt tt seconds after it was launched if there was no gravity.

Sample Response

  1.  
    seconds 0 1 2 3 4 5 tt
    distance above ground (feet) 5 95 185 275 365 455 5+90t5+90t
  2. d=5+90td=5+90t
Activity Synthesis (Teacher Notes)

The goal is to make sure students understand that without gravity the height will follow a linear pattern. Ask students how the values in the table are changing and what equation would describe the height of the t-shirt if there were no gravity. Even without graphing, students should notice that the height of the t-shirt over time is a linear function given the repeated addition of 90 feet every time tt increases by 1.

Tell students that, in the next activity, they will look at some actual heights of the t-shirt.

Standards
Addressing
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • F-BF.1·Write a function that describes a relationship between two quantities
  • HSF-BF.A.1·Write a function that describes a relationship between two quantities.

15 min

15 min