# Math Ia Pascals Triangles

Topics: Quadratic equation, Integer, Negative and non-negative numbers Pages: 5 (576 words) Published: February 3, 2013
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

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
-3b+6= 4a-b+3
6= 4a +2b +3
0= 4a +2b -3
-2b = 4a-3
b= -2a+ 3.
2
This will be known as equation 9

• substitute equation 9 to equation 7
-2a+ 3 = -4a+ 5 +c
2 2
2a + 3 = 5 +c
2. 2
2a=4+c
a=2+ 1 c
2
This will be known as equation 10

• substitute equation 7 to equation 8

b= -4a+ 5 - 9 a-3b+6
2
b= -13a – 3b + 17
2
4b= -13a + 17
2
b= -13 a + 17
4 8
This will be known as equation 11

• substitute equation 9 to equation 11

-2 a + 3 = -13 a + 17
2 14 8
-2a = -13 a + 5
4 8
5 a = 5
4 8
a= 1
2
• substitute the answer of a to equation 9

b= (-2) 1 + 3.
2. 2
b= -1 + 3
2
b= 1
2

• substitute the answer for a and for b to equation 8
c= (-9) 1 * (-3) 1 +6
2. 2
c= -9 - 3 +6
2. 2
c= -6+6
c=0

• a= 1 b= 1 c= 0
2 2

• y = 1 x2 + 1 x
2. 2

• Check:

1. 1= 1 (1)2 + 1 (1)
2 2
1= 1

2. 3 = 1 (2)2 + 1 (2)
2 2
3= 3

3. 6 = 1 (3)2 + 1 (3)
2 2
6= 6

4. 10 = 1 (4)2 + 1 (4)
2 2
10= 10

5. 15 = 1 (5)2 + 1 (5)...