### Student Page 4.5.5 Tiling Tables

#### 1.

Kelly makes square tables and then tiles the tops. To cover the tabletops, she uses quarter tiles for each corner, half tiles along the sides, and full square tiles to fill in the rest. The first 5 sizes in her line of tabletops are shown in Figure 4.5.5.1. Both side lengths of the first tabletop are 10 inches.

##### (a)

Complete Table 4.5.5.2 for the first 6 tabletops.

##### (b)

Look for patterns in Table 4.5.5.2. Describe at least 3 patterns you see in the data.

#### 2.

Let the table number, \(n\text{,}\) be the independent variable. Plot the data in the columns indicated. Analyze the data in the table. Determine to what function family the data belongs. Explain how you know.

##### (a)

Columns A and B:

##### (b)

Columns A and C:

##### (c)

Columns A and D:

##### (d)

Columns A and E:

#### 3.

Find equations for each set of data in Student Page Exercise 4.5.5.2. Enter the equations into the last row of Table 4.5.5.2.

#### 4.

##### (a)

Write any quadratic equations in standard form.

##### (b)

Is it possible to factor the quadratic equation? Why or why not?

##### (c)

Subtract the constant from the standard form of the equation. Write this new equation.

##### (d)

Compare the graph of the equation in Student Page Exercise 4.5.5.4 to the graph of the equation in Task 4.5.5.4.c. How do these graphs comapre with each other? How do you know?

##### (e)

Factor the equation you found in Task 4.5.5.4.c.

##### (f)

Find the vertex of the equation in Task 4.5.5.4.c from the factored form of the equation (in Task 4.5.5.4.e).

##### (g)

How does this vertex relate to the vertex of the equation in Student Page Exercise 4.5.5.4. Find the vertex of the equation in Student Page Exercise 4.5.5.4

##### (h)

Write the vertex form of the quadratic equation in Student Page Exercise 4.5.5.4.

##### (i)

Show that the equations in Student Page Exercise 4.5.5.4 and Task 4.5.5.4.h are equivalent.