Quadratic Formula

Falc oner Football
It’s October and high school football is back. The coach challenged our math class to figure out
what the area of the field is. The coach estimated the dimensions of a football field in yards².
There’s only one problem, he decided to give the dimensions to the coach as 4x + 2 yards by 2x + 1
yards. Thus, we must figure out the area in terms of x .

To do this, fill in the football field be low with Algebra Tiles. Make sure that the edge lengths
match up to the tiles in each row or column.

Now, add up the amount of each kind of tile you have. This should re present the area of the
football field in terms of x.

Area =

Finally, the coach told us that x = 29.5 yards. So what is the actual area in yards²?

Grid Multiplication with Tiles
Let’s see how we can multiply binomials to obtain trinomials using a new technique.

Example 1:
Consider 2 binomials (2x + 2) and (3x + 1).

Setup: Use algebra tiles and grid worksheet to set up a multiplication grid as follows.

Represents an x².Represents an x. Represents a 1

Use each tile as a row or a column to multiply. For example in the first row, first column, you would
get x * x = x². Then place an x² tile in the appropriate spot.

Fill in the rest of the chart.

Then, record your findings below.

2._______________ Number of x ² tiles. Now write the product below :
3._______________Number of x tiles.
4._______________Number of 1 tiles. 5.______________________________

Example 2:
Note: Black Tiles represent negatives.
When multiplying negatives, remember to make the signs agree .
For Example: -x * 1 = -x so make sure to use a negative x tile .
Work in groups to fill in the chart and answer questions.

6. What are the factors ? _______________ and ______________.
7. Fill in the grid on your worksheet.

8. _______________Number of x² tiles. Now write the product below:
9. _______________Number of x tiles.
10._______________Number of 1 tiles. 11.______________________________
Example 3:
12. Factors: ______________ and _____________.
13. Fill in the grid.

14. Final product: ______________________

Multiply Trinomials!!!
Example 4:
Fill in the charts the same way we did when we used algebra tiles.
Remember, when multiplying exponents to add the exponents.

Combine like terms by adding the coefficients.
16. Coefficient of x⁴ terms: _____________.19. Coefficient of x terms:_____________.
17. Coefficient of x³ terms:_____________. 20. Sum of constant terms:____________.
18. Coefficient of x² terms:_____________.

Use 16.-20. to write your final product.

21. ___________________________

Example 5:
22. Fill in the grid.

Combine like terms by adding the coefficients.
23. Coefficient of x⁴ terms: ____________.26. Coefficient of x terms:_____________.
24. Coefficient of x³ terms: ____________.27. Sum of constant terms:____________.
25. Coefficient of x² terms:_____________.

Use 23.-27 to write your final product.

28. ___________________________