### Student Page4.5.5Tiling Tables A4US

#### 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.

Columns A and B:

Columns A and C:

Columns A and D:

Columns A and E:

#### 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.

##### (e)

Factor the equation you found in Task 4.5.5.4.c.