Math & climate change

Demonstrated

by:

Demonstrated

by:

Math & Climate Change

“Things we can do for global warming using Quadratic

Equation”

Math & Climate Change

“Things we can do for global warming using Quadratic

Equation”

Ramil P. Polintan

Ramil P. Polintan

Student, Ph.D. E.M.

Y

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CLIMATE MATH(In the tune of Top of the World)

COME AND JOIN OUR MATHEMATICS CLASSAND YOU’LL SURELY ENJOY BEING WITH US

MASTERING BASIC FACTS, MULTIPLY, ADD, SUBTRACTEVERYTHING HAS BEEN LEARNED THE EASY WAY.

COMBINING MATHEMATICS AND CLIMATELET US GRAPH QUADRATIC FUNCTION AT ALL TIMES

LEARN WITH EASE AND SUCCESS MAKE US DO OUR BESTMODERN MATH TODAY IS MAKING DIFFERENCE.

(Refrain 2x)

I’M ON THE TOP OF THE WORLD GRAPHING, DOWN IN THE LAND OF NUMBERS

PLANTING TREES IS BETTER WAYTO REDUCE GREENHOUSE GASSES AND ABSORB CARBON

DIOXIDE FROM THE AIRCOME BE HAPPY AND HAVE FUN CLIMATE MATH.

Watching “Now is the Time

”

Guide Questions/Exploration Based on Documentary Video

1. What is global warming?2. Why there is a global

warming?3. How will climate change?4. Can the climate change by

us?5. What is greenhouse effect?6. What are the source of

greenhouse gasses?7. When do you send green

house gasses into the air?8. What are the impacts of

climate change?9. Can you make a difference?10. How can we make our planet

a better place?11. What are the efforts to control

climate change?12. Can tree planting helps?

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..

.

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..Vertex (0,0)

f(x) = X

. .

. .

f(x) = 2X

....

f(x) =1/2 X

2

2

2

Axis of symmetry

As the value of a > 1 or increases,

the parabola becomes narrower.

As the value of a < 1 or decreases,

the parabola becomes wider

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..

.

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..Vertex (0,0)

f(x) = X

f(x) = -X2

2

Axis of symmetry

if a > 0, the graph opens upward and the function attains a minimum value.

if a < 0, the graph opens downward and the function attains a maximum value.

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..

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..Vertex (0,0)

f(x) = X

. .f(x) = X + 4

f(x) = X - 6

2

2

2

Axis of symmetry

The graph of f(x) = x + k

2

f(x) = x²

f(x) = (x – 0)²

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f(x) = (X + 5)

2

f(x) = (X – 2)

2

Vertex (2, 0)Vertex (-5, 0)

Axis of symmetry x= 2Axis of symmetry x= -5

f(x) = X

2

Vertex (0, 0)

The graph of f(x) = (x-h)

2

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f(x) = (X + 8) - 6

2 f(x) = (X – 4) + 3

2

Vertex (4, 3)

Vertex (-8,- 6)

Axis of symmetry x= 4

Axis of symmetry x= -8

f(x) = X

2

Vertex (0, 0)

The graph of f(x) = a(x-h) + k

2

Where,(h, k) is the vertex h=k is the line of symmetry

SHOW VARIOUS GRAPH/PARABOLA

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f(x) = -(X + 8) + 152 f(x) = (X – 5) - 6

2

Vertex (5, -6)

Vertex (-8, 15)

X= 5

x= -8

f(x) = (X + 3) - 4 2

Vertex (-3, -4)

X = -3

SHOW VARIOUS GRAPH/PARABOLA

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f(x) = -X + 92

f(x) = (X – 7) + 2

2

Vertex (7, 2)

Vertex (0, 9)

X= 7

x= 0

f(x) = (X + 10) 2

Vertex (-10, 0) X = -10

f(x) = (X + 4)²

Vertex (-4, 0) X = -4

f(x) = 2(X + 4)²

Vertex (-4, 0) X = -4

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..

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..Vertex (0,0)

f(x) = X

. .

. .

f(x) = 2X

....

f(x) =1/2 X

2

2

2

Axis of symmetry

The graph of f(x) = ax

2

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.Vertex (-4,0)

f(x) = (X + 4)²

.

f(x) = 2(X + 4)²

X = -4

CULMINATING ACTIVITY•Complete the table and graph each of the following function by shifting the vertex using the graphing board.

Quadratic Function Vertex Equation of axis of symmetry

1. f(x) = X²+ 3

2. f(x) = -2X²+ 3

3. f(x) = (X - 3)²

4. f(x) = (X - 7)²

5. f(x) =-(X + 4)² + 2

6. f(x) = (X - 9)² - 11

7. f(x) = 2(X + 3)² + 5

8. f(x) = ½ (X + 8) ² + 4

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..Vertex (0,0)

f(x) = X2

Generalization

The graph of quadratic

function (f(x) =x² is a parabola

with the vertical axis (the y-

axis or line x = 0) as its line of

symmetry and its vertex is (0,

0).

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..

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..Vertex (0,0)

f(x) = X

. .

. .

f(x) = 2X

....

f(x) =1/2 X

2

2

2

• If a>1, then the parabola is narrower than f(x) = x².

• If a< than 1, then the parabola is wider than f(x) = x².

Generalization

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..Vertex (0,0)

f(x) = X2

Generalization

If a>0, then the parabola opens

upward.

f(x) = -X²

If a<0, then the parabola opens

downward.

Source: PAGASA

Gapan, N. EcijaNovember 14, 2004

Forming function to Reforest Mountain based

on f(x) = (x – h)² + k

f(x) =

-(X + discipline)²

+tree planting

f(x) = -(X + discipline)² + Tree Planting

Vertex ( D, TP)

X = Tree Planting

TREE PLANTING ACTIVITY

The importance/application of Quadratic Function in real Life: Where the quadratic equation (f(x) = -(x + discipline) 2 +

Tree planting will be used as our function to reforest the

mountains.

ASSIGNMENT

1. Find other places where we can conduct tree planting activity.

2. Make another quadratic function to make a difference.