The document discusses using a quadratic function f(x) = -(x + discipline)2 + tree planting to model reforesting mountains, where x represents tree planting, the vertex is (discipline, tree planting), and increasing discipline results in fewer trees planted. It also assigns using this function to plan a tree planting activity that applies quadratic functions to environmental issues.

1. Y
X

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 TIMES
LEARN 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 WAY
TO REDUCE GREENHOUSE GASSES AND ABSORB CARBON
DIOXIDE FROM THE AIR
COME BE HAPPY AND HAVE FUN CLIMATE MATH.

3. Watching “Now
is the Time”

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. . .
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. Y
9 10 11 12 13 14 15 16 17
Axis of symmetry
2
. .
if a > 0, the graph f(x) = X
opens upward and
the function attains
8
a 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)
2
if a < 0, the graph f(x) = -X
opens downward and
the function attains a
maximum value.

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
. .
6
The 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. f(x) = x²
f(x) = (x – 0)²

9. Y
9 10 11 12 13 14 15 16 17
2
f(x) = (X + 5) f(x) = X2
2
f(x) = (X – 2)
8
7
6
5
4
3
Axis 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. Y
9 10 11 12 13 14 15 16 17
f(x) = X2
2
2 f(x) = (X – 4) + 3
f(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) + k
Vertex (-8,- 6) Where,(h, k) is the vertex
h=k is the line of symmetry

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) - 6
f(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. 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 12
Vertex (-10, 0) -9 -8 -7 -6 -5 -4 -3 -2 -1
X = -10
2
f(x) = -X + 9

13. f(x) = (X + 4)²
Vertex
X = -4
(-4, 0)
f(x) = 2(X + 4)²
Vertex
X = -4
(-4, 0)

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. Y
9 10 11 12 13 14 15 16 17
f(x) = 2(X + 4)²
f(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. 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

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
. .
6
x = 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. . .
2
Y
9 10 11 12 13 14 15 16 17
f(x) = 2X
Generalization
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. Y
9 10 11 12 13 14 15 16 17
Generalization
2
. .
f(x) = X
If a>0, then the
8
parabola 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 -1
parabola opens downward.
f(x) = -X²

20. Gapan, N. Ecija
November 14, 2004
Source: PAGASA

22. Forming function to Reforest
Mountain based on
f(x) = (x – h)² + k
f(x) = -(X + discipline)² +tree
planting

23. X = Tree Planting
Vertex ( D, TP)
f(x) = -(X + discipline)² + Tree Planting

25. 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.

26. ASSIGNMENT
1. Find other places where we
can conduct tree planting
activity.
2. Make another quadratic
function to make a
difference.