Post on 27-May-2015
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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
X
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?
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
.
..
.
.
..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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
.
..
.
.
..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.
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
.
..
.
.
..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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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..
.
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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).
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
.
..
.
.
..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
Y
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18-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
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..
.
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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.