Designing a Garden In this activity, you will apply mathematics to problems arising in everyday life and communicate mathematical ideas using multiple representations.

Part A
Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden’s width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Question 1
Question
Write expressions to represent the length and width of Melissa’s vegetable garden in terms of x.

Enter the correct answer in the box.


Question 2
Question
Write an expression to represent the perimeter of Melissa’s garden in terms of x.

Type the correct answer in each box. Use numerals instead of words.

Perimeter:

Question 3
Question
If the area of the vegetable garden is 170 square feet, which equation could be use to find the length of the tomato patch?

Select the correct answer.

Question 4
Question
Melissa wants to make a table representing the area of her vegetable garden for a variety of different lengths of the tomato patch. She uses her area expression to create the table.

Complete the table by typing the correct answer in each box. Use numerals instead of words. Do not round your decimal answers.

Length of Tomato Patch
(in feet) Area of Vegetable Garden
(in square feet)
338
6.5
147.25
7
Part B
Melissa reserves another rectangular patch in her vegetable garden for growing bell peppers. Since the space that she can reserve for a rectangular bell pepper patch depends on how large she makes the tomato patch, she uses function p to represent the area of the bell pepper patch, where x is the length of the tomato patch.

graph of function p(x) = -0.5x^2 + 6x

Question 1
Question
Select the correct answer from each drop-down menu.

Function p is a
function.

When the length of the tomato patch is 8 feet, the area of the bell pepper patch is
square feet.

The maximum possible area of the bell pepper patch is
square feet when the length of the tomato patch is
feet.

Question 2
Question
Match the real-world descriptions with the features they represent within the context of Melissa’s garden. Not all tiles will be used.

Tiles
length of the tomato patch when
the area of the bell pepper patch
is 0
all possible lengths of the tomato
patch
area of the tomato patch when the
length of the bell pepper patch is 0
all possible areas of the bell pepper
patch
area of the bell pepper patch when
the length of the tomato patch is 0
all possible areas of the tomato
patch
Pairs
x-intercepts
arrowBoth
y-intercept
arrowBoth
domain
arrowBoth
range
arrowBoth
Question 3
Question
What are the domain and range of function p within the context of Melissa’s garden?

Drag the values to the correct locations on the image. Each value can be used more than once, but not all values will be used.