Lesson 4 Rabbit Run Solidify Understanding

Learning Focus

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

Identify features of a function from a graph.

Are all quadratic functions increasing?

Are all quadratic functions discrete?

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.

a blank 17 by 17 grid

4.

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

5.

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

Ready for More?

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?

Takeaways

Is this a quadratic function?

Vocabulary

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.

1.

2.

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

3.

Two linear functions labeled fx and gx on the same coordinate plane. fx passes through (0, 5) and (5, 5). gx passes through (0, -2) and (3, 0). x–10–10–10–5–5–5555101010y–10–10–10–5–5–5555101010000

4.

two exponential functions on a coordinate plane labeled f of x and g of x x–5–5–5555y555000