# Math Ia Pascals Triangles

**Topics:**Quadratic equation, Integer, Negative and non-negative numbers

**Pages:**5 (576 words)

**Published:**February 3, 2013

• 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

-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)...

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