# Lesson 3Scott’s Muscle MarchSolidify Understanding

## Learning Focus

Model a quadratic function with tables, graphs, and equations.

Understand the first difference of a quadratic function.

How can a quadratic function be built from a linear function?

## Open Up the Math: Launch, Explore, Discuss

Scott was determined to eat right and get in shape. He joined a gym and added push-ups to his daily exercise routine. He started keeping track of the number of push-ups he completed each day in the bar graph, with day one showing he completed three push-ups. After four days, Scott was certain he could continue this pattern of increasing the number of push-ups for at least a few months.

### 1.

Model the number of push-ups Scott will complete on any given day. Include both explicit and recursive equations.

Scott’s gym is sponsoring a “Muscle March” promotion. The goal of “Muscle March” is to raise money for charity by doing push-ups. Scott has decided to participate and has sponsors that will donate money to the charity if he can do a total of at least 500 push-ups, and they will donate an additional \$10 for every 100 push-ups he can do beyond that. So now Scott is going to track the total number of push-ups done up to any given day of the month.

### 2.

Estimate the total number of push-ups that Scott will do in a month if he continues to increase the number of push-ups he does each day in the pattern shown.

### 3.

Draw the diagram that shows the total number of push-ups that Scott has done in the month at the end of each day.

### 4.

How many push-ups will Scott have done after a week?

### 5.

Model the total number of push-ups that Scott has completed on any given day during “Muscle March.” Include both recursive and explicit equations.

## Ready for More?

Will Scott meet his goal and earn the donation for the charity? Will he get a bonus? If so, how much? Explain.

## Takeaways

Characteristics of Quadratic Functions:

## Lesson Summary

In this lesson we modeled a situation with a diagram, table, graph, and equations. We learned that quadratic functions can be models for the sum of an arithmetic sequence and furthered our understanding of the type of change exhibited by quadratic functions.

## Retrieval

Multiply using the distributive property. Then add like terms.

### 2.

Write the first five terms of the sequences defined by the recursive rule.