## Act 1

1. How fast was the car going when the speedometer got stuck?

2. Write down a guess.

I found this while browsing the Illustrative Mathematics website. It’s taken from their “Braking Distance” task.

## Act 2

3. What information would be useful to figure this out?

4. Write down some questions you have in your head right now.

The lesson can be used in an Algebra 1 or 2 class (among others). The kids can utilize the information from Act 1 to make predictions. Also, here is extra data to help.

In addition, it’d be helpful to have them model the situation in Desmos. Here’s a sample graph.

However, it’d probably be beneficial to give them a chance to reason through the extra data first before jumping into Desmos. The students may pick up on the common second difference for the braking distance. From there, they could continue the pattern until the final stopping distance is reached.

For Algebra 2, the teacher may choose to use the same approach, or he could have the kids write equations based on 3 coordinates or a given vertex and point (see the sequel below). This is what I originally had in mind when creating the task. It’d be nice to create a need for writing equations of quadratic functions.

## Act 3

## Sequel

5. If the vertex is (-21, -22.05), write an equation to describe the braking distance data.

6. Write an equation to describe the braking distance data by using 3 coordinates.

**Common Core Standards**

HSF.LE

Construct and compare linear, quadratic, and exponential models and solve problems.

HSF.BF.A.1

Write a function that describes a relationship between two quantities.

**TEKS**

A.8(B)

write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

2A.4(B)

write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening