# Lesson 4Rabbit RunSolidify Understanding

## Learning Focus

Model a story context with table, graph, and equation.

Identify features of a function from a graph.

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

Misha has a new rabbit that she named Wascal. She wants to build Wascal a pen so that the rabbit has space to move around safely. Misha has purchased a 72 foot roll of fencing to build a rectangular pen.

### 1.

If Misha uses the whole roll of fencing, what are some of the possible dimensions of the pen?

### 2.

If Misha wants a pen with the largest possible area, what dimensions should she use for the sides? Justify your answer.

### 3.

Write a model for the area of the rectangular pen in terms of the length of one side. Include both an equation and a graph.

### 4.

What kind of function is this? How do you know?

### 5.

How does this function compare to the quadratic function in I Rule?

If the rabbit pen does not need to be a rectangle, is there a way to get more area with of fencing around the perimeter?

## Lesson Summary

In this lesson we examined a quadratic function that was a model for area but had many different features than those we have seen previously. We learned that all quadratic functions have a linear rate of change and constant second difference, but some may be continuous and have intervals of increase and decrease depending on the domain.

## Retrieval

Find the slope between the given points.

### 2.

Determine which function will be changing faster for large values of on each graph.