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# Math & climate change

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Learn about math and climate, how quadratic equation be applied to climate change, you will learn about the issues of climate change and global warming through watching documentary, how humans affect global warming, and things you can do to stop it.

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### Math & climate change

1. 1. Y X
2. 2. CLIMATE MATH (In the tune of Top of the World) COME AND JOIN OUR MATHEMATICS CLASS AND YOU’LL SURELY ENJOY BEING WITH US MASTERING BASIC FACTS, MULTIPLY, ADD, SUBTRACT EVERYTHING HAS BEEN LEARNED THE EASY WAY. COMBINING MATHEMATICS AND CLIMATE LET US GRAPH QUADRATIC FUNCTION AT ALL TIMESLEARN WITH EASE AND SUCCESS MAKE US DO OUR BEST MODERN 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 AIR COME BE HAPPY AND HAVE FUN CLIMATE MATH.
3. 3. Watching “Now is the Time”
4. 4. 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?
5. 5. . . 2 Y 9 10 11 12 13 14 15 16 17 f(x) = 2X Axis of symmetry 2 . . f(x) = X . . 8 2 .. .. 7 f(x) =1/2 X 6 5 .. .. 4 3 . 2 1 0 -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) -9 -8 -7 -6 -5 -4 -3 -2 -1 As the value of a > 1 or As the value of a < 1 or increases, decreases,the parabola becomes narrower. the parabola becomes wider
6. 6. Y 9 10 11 12 13 14 15 16 17 Axis of symmetry 2 . .if a > 0, the graph f(x) = Xopens upward andthe function attains 8a minimum value. 7 . . 6 5 4 . .. 3 2 1 0-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (0,0) 2if a < 0, the graph f(x) = -Xopens downward andthe function attains amaximum value.
7. 7. . . 2 Y 9 10 11 12 13 14 15 16 17 f(x) = X + 4 Axis of symmetry 2 . . f(x) = X 8 7 . . 6The graph of f(x) = x2+ k 2 5 f(x) = X - 6 4 . .. 3 2 1 0 -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 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (0,0)
8. 8. f(x) = x²f(x) = (x – 0)²
9. 9. Y 9 10 11 12 13 14 15 16 17 2f(x) = (X + 5) f(x) = X2 2 f(x) = (X – 2) 8 7 6 5 4 3Axis of symmetry x= -5 2 Axis of symmetry x= 2 1 0 -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 (-5, 0) Vertex (2, 0) Vertex (0, 0) -9 -8 -7 -6 -5 -4 -3 -2 -1 2 The graph of f(x) = (x-h)
10. 10. Y 9 10 11 12 13 14 15 16 17 f(x) = X2 2 2 f(x) = (X – 4) + 3f(x) = (X + 8) - 6 8 7 6 Axis of symmetry x= 4 5 4 3 Vertex (4, 3)Axis of symmetry x= -8 2 1 0 -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) -9 -8 -7 -6 -5 -4 -3 -2 -1 2 The graph of f(x) = a(x-h) + kVertex (-8,- 6) Where,(h, k) is the vertex h=k is the line of symmetry
11. 11. Y 9 10 11 12 13 14 15 16 17 Vertex (-8, 15) x= -8 2 f(x) = (X + 3) - 4 2 2 f(x) = (X – 5) - 6f(x) = -(X + 8) + 15 SHOW VARIOUS 8 7 GRAPH/PARABOLA 6 5 4 3 2 1 0 -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 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (-3, -4) X = -3 Vertex (5, -6) X= 5
12. 12. Y 9 10 11 12 13 14 15 16 17 x= 0 Vertex (0, 9) 2 2 f(x) = (X – 7) + 2 f(x) = (X + 10) SHOW VARIOUS 8 7 GRAPH/PARABOLA 6 5 4 3 2 Vertex (7, 2) X= 7 1 0-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12Vertex (-10, 0) -9 -8 -7 -6 -5 -4 -3 -2 -1 X = -10 2 f(x) = -X + 9
13. 13. f(x) = (X + 4)² Vertex X = -4 (-4, 0) f(x) = 2(X + 4)²Vertex X = -4(-4, 0)
14. 14. . . 2 Y 9 10 11 12 13 14 15 16 17 f(x) = 2X Axis of symmetry 2 . . f(x) = X . . 8 2 .. .. 7 f(x) =1/2 X 6 5 .. .. 4 3 . 2 1 0-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (0,0) The graph of f(x) = ax2
15. 15. Y 9 10 11 12 13 14 15 16 17 f(x) = 2(X + 4)²f(x) = (X + 4)² . 8 7 . 6 5 4 3 . 2 1 0-12 -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 (-4,0) X = -4 -9 -8 -7 -6 -5 -4 -3 -2 -1
16. 16. 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 symmetry1. f(x) = X²+ 32. f(x) = -2X²+ 33. f(x) = (X - 3)²4. f(x) = (X - 7)²5. f(x) =-(X + 4)² + 26. f(x) = (X - 9)² - 117. f(x) = 2(X + 3)² + 58. f(x) = ½ (X + 8) ² + 4
17. 17. Y 9 10 11 12 13 14 15 16 17 Generalization The graph of quadratic function 2 . . f(x) = X (f(x) =x² is a parabola with the vertical axis 8 (the y-axis or line 7 . . 6x = 0) as its line of 5 symmetry and its 4 vertex is (0, 0). . .. 3 2 1 0-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (0,0)
18. 18. . . 2 Y 9 10 11 12 13 14 15 16 17 f(x) = 2XGeneralization 2 . . f(x) = X . . 8 2 .. .. 7 f(x) =1/2 X 6 5 .. .. 4 3 . 2 1 0-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -9 -8 -7 -6 -5 -4 -3 -2 -1 Vertex (0,0) •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.
19. 19. Y 9 10 11 12 13 14 15 16 17 Generalization 2 . . f(x) = X If a>0, then the 8parabola opens upward. 7 . . 6 5 4 . .. 3 2 1 0 -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) If a<0, then the -9 -8 -7 -6 -5 -4 -3 -2 -1parabola opens downward. f(x) = -X²
20. 20. Gapan, N. Ecija November 14, 2004Source: PAGASA
21. 21. Forming function to Reforest Mountain based on f(x) = (x – h)² + kf(x) = -(X + discipline)² +tree planting
22. 22. X = Tree Planting Vertex ( D, TP)f(x) = -(X + discipline)² + Tree Planting
23. 23. TREE PLANTING ACTIVITY The importance/application of Quadratic Function in real Life: Where the quadratic equation (f(x) = -(x + discipline) 2 + Treeplanting will be used as our function to reforest the mountains.
24. 24. ASSIGNMENT1. Find other places where we can conduct tree planting activity.2. Make another quadratic function to make a difference.