Math Ia Pascals Triangles

Practice Math IA

• Each set of steps above is composed of 1x1 squares • Show what 4 steps and 5 steps look like

• ‘n’ represents the number of steps • Find the area for n= 1,2,3,4,5

Step 1: Step 2: Step 3: Step 4: Step 5:
12 = 1 12 x 3 = 3 1 2 x6 = 6 1 2x10 = 10 12x 15 =15

|Steps (n) |Area |
| |(y) |
|1 |1 |
|2 |3 |
|3 |6 |
|4 |10 |
|5 |15 |

• Display results in a table. Using technology, display your results in a discrete graph

• Find a quadratic function that shows the relationship between the number of steps and the area

Quadratic Formula:

y= ax2 + bx+ c
[pic]

• Plug in the coordinates to the quadratic formula

1) 1= a (1)2 +b (1) – c 2) 3= a(2)2 b(2) +c 3) 6=a(3)2 +b(3) +c 1= a+ b+ c 3=4a+2b+c 6= 9a+3b+ c

4) 10=a (4)2 +b (4) + c 5) 15= a (5)2 +b (5)+c 10= 16a+ 4b +c 15= 25a+ 5b +c

• Solve for c in equation 5 15= 25a+ 5b+c 15-c= 25a+b 3-c= 5a+b -c= 5a+b-3 c= -5a –b+3
This will be known as equation 6

• Solve for b using equation 4 10=16a+4b+c 10+4b=16a+c -5 + b= -4a +c 2 b= -4a+ 5 + c 2
This will be known as equation 7

• Solve for c using equation 3 6=9a+3b+c -c+6 = 9a+3b -c =9a + 3b -6 c= -9 a-3b+6
This will be known as equation 8

• substitute equation 8 to equation 6 -9a -3b+ 6= -5a – b+3