contoh excel 2

7/29/2019 contoh excel 2

1/17

Exploring the Family of Quadratic Functions

Objective: To examine the vertex and standard forms of the

quadratic function.

Developed as part of a presentation at MCTM 2007 Conference.

Click on the tabs to navigate!


2/17

Vertex Form of Quadratic y = a(x-h)2 + k

a = 1 h = 0 k = 0

x y y = x2

a

-25 625 625 0 51

-24 576 576 0 -50 50

-23 529 529 0 vertex (h, k) axis of symmetry h

-22 484 484 0 h k x y 20

-21 441 441 0 -50 0 -50 625 -20 20

-20 400 400 0 -50 0 k

-19 361 361 0 -50 -625 5000

-18 324 324 0 -50 0 -5000 5000

-17 289 289 0

-16 256 256 0

-15 225 225 0

-14 196 196 0

-13 169 169 0

-12 144 144 0

-11 121 121 0

-10 100 100 0

-9 81 81 0

-8 64 64 0

-7 49 49 0

-6 36 36 0 FALSE FALSE

-5 25 25 0

-4 16 16 0 FALSE y = ax + bx + c

-3 9 9 0

-2 4 4 0 Sinex 2007

-1 1 1 0

y = 0

-800

-600

-400

-200

0

200

400

600

800

-25 -20 -15 -10 -5 0 5 10 15 20 25y

x

show the vertex show the axis of symmetry

See the standard form of the quadratic function
http://academic.pgcc.edu/~ssinexhttp://academic.pgcc.edu/~ssinex


3/17

0 0 0 0

1 1 1 0

2 4 4 0

3 9 9 04 16 16 0

5 25 25 0

6 36 36 0

7 49 49 0

8 64 64 0

9 81 81 0

10 100 100 0

11 121 121 0

12 144 144 0

13 169 169 0

14 196 196 0

15 225 225 0

16 256 256 0

17 289 289 0

18 324 324 0

19 361 361 0

20 400 400 0

21 441 441 0

22 484 484 0

23 529 529 0

24 576 576 0

25 625 625 0


4/17

Standard Form of Quadratic y = ax2 + bx + c

a = 1 b = 0 c = 0

x y y = x2

-25 625 625 0

-24 576 576 0

-23 529 529 0

-22 484 484 0

-21 441 441 0 roots slope roots

-20 400 400 0 0.00 0 0.2 0.04 x1 = 0.00

-19 361 361 0 0.00 0 0 0

-18 324 324 0 -0.2 0.04 x2 = 0.00

-17 289 289 0

-16 256 256 0

-15 225 225 0 double roots

-14 196 196 0

-13 169 169 0 x = 0

-12 144 144 0 25

-11 121 121 0 slope = 0

-10 100 100 0

-9 81 81 0-8 64 64 0

-7 49 49 0

-6 36 36 0 FALSE y = ax2 + bx + c

-5 25 25 0

-4 16 16 0

-3 9 9 0

-2 4 4 0 Sinex 2007

-1 1 1 0

y = 0

0

100

200

300

400

500

600

700

-25 -20 -15 -10 -5 0 5 10 15 20 25

y

x

See the standard form of the quadratic function


5/17

0 0 0 0

1 1 1 0

2 4 4 0 Note: You cannot name a variable with the letter "c"!

3 9 9 04 16 16 0

5 25 25 0

6 36 36 0

7 49 49 0

8 64 64 0

9 81 81 0

10 100 100 0

11 121 121 0

12 144 144 0

13 169 169 0

14 196 196 0

15 225 225 0

16 256 256 0

17 289 289 0

18 324 324 0

19 361 361 0

20 400 400 0

21 441 441 0

22 484 484 0

23 529 529 0

24 576 576 0

25 625 625 0


6/17


7/17

Looking at Differences y = ax2 + bx + c

First Second a = 1 b = 0 c = 0

x y Dy/Dx Dy/Dx average tim

-25 625 -500 -500 -24.5-24 576 -500 -500 -23.5

-23 529 -500 -500 -22.5

-22 484 -500 -500 -21.5

-21 441 -500 -500 -20.5

-20 400 -500 -500 -19.5

-19 361 -500 -500 -18.5

-18 324 -500 -500 -17.5

-17 289 -500 -500 -16.5-16 256 -500 -500 -15.5

-15 225 -500 -500 -14.5

-14 196 -500 -500 -13.5

-13 169 -500 -500 -12.5

-12 144 -500 -500 -11.5

-11 121 -500 -500 -10.5

-10 100 -500 -500 -9.5

-9 81 -500 -500 -8.5-8 64 -500 -500 -7.5

-7 49 -500 -500 -6.5

-6 36 -500 -500 -5.5

-5 25 -500 -500 FALSE FALSE -4.5

-4 16 -500 -500 -3.5

-3 9 -500 -500 -2.5

-2 4 -500 -500 Sinex 2007 -1.5

-1 1 -500 -500 -0.5

y = x2 + 1E-14x + 6E-13

y = - 500 y = - 500-300

-200

-100

0

100

200

300

-25 -20 -15 -10 -5 0 5 10 15 20 25

y

x

calculate and plot the first difference calculate and plot the second difference


8/17

0 0 -500 -500 0.5

1 1 -500 -500 1.5

2 4 -500 -500 Note: The first and second differences are plotted against the 2.5

3 9 -500 -500 average time, which is in column L and hidden as white font. 3.54 16 -500 -500 4.5

5 25 -500 -500 5.5

6 36 -500 -500 6.5

7 49 -500 -500 7.5

8 64 -500 -500 8.5

9 81 -500 -500 9.5

10 100 -500 -500 10.5

11 121 -500 -500 11.5

12 144 -500 -500 12.5

13 169 -500 -500 13.5

14 196 -500 -500 14.5

15 225 -500 -500 15.5

16 256 -500 -500 16.5

17 289 -500 -500 17.5

18 324 -500 -500 18.5

19 361 -500 -500 19.5

20 400 -500 -500 20.5

21 441 -500 -500 21.5

22 484 -500 -500 22.5

23 529 -500 -500 23.5

24 576 -500 24.5

25 625


9/17

e


10/17

Baseball Pop-up (travels vertically only) How high will the baseball rise?

Select the astronomical object

initial height = 0 initial velocity = 20 acceleration = 9.81 m/sec2

time, t height, h ho (m) vo (m/sec) a = -g 40 0.00

0.06 1.18

0.12 2.33 object g maximum

0.18 3.44 1 Sun . height

0.24 4.52 1 0 0 0 2 Mercury 3.59 20.39 m

0.3 5.56 1 20.38735 3 Venus 8.87

0.36 6.56 1 0 4 Earth 9.81 velocity

0.42 7.53 1 0 5 - Moon1.62

20.00 m/sec0.48 8.47 6 Mars 3.77 For t=0, initial velocity

0.54 9.37 7 Jupiter 25.95

0.6 10.23 8 Saturn 11.08

0.66 11.06 9 Uranus 10.67

0.72 11.86 10 Neptune . hang time

0.78 12.62 11 Pluto 0.42 4.08 sec

0.84 13.34

0.9 14.03 Can you relate the ho, vo and g to the regression equation? answer

0.96 14.68

1.02 15.30 time step = 0.06 time = 0 0

1.08 15.88 height = 0.00 tracer point

1.14 16.43 Adjust the time step to get the complete

1.2 16.94 time until the baseball hits the ground. ( with constant acceleration due to gravity)

1.26 17.41

1.32 17.85 Sinex 2007

1.38 18.26 g-values: http://aerospaceweb.org/question/astronomy/q0227.shtml

y = -4.905x2 + 20x - 3E-14

0

5

10

15

20

25

0 2 4 6 8

height

time

0

5

10

15

20

25

Path of

Baseball


11/17

1.44 18.63

1.5 18.96

1.56 19.26

1.62 19.531.68 19.76

1.74 19.95

1.8 20.11

1.86 20.23

1.92 20.32

1.98 20.37

2.04 20.39

2.1 20.37

2.16 20.32

2.22 20.23

2.28 20.10

2.34 19.94

2.4 19.75

2.46 19.52

2.52 19.25

2.58 18.95

2.64 18.61

2.7 18.24

2.76 17.84

2.82 17.39

2.88 16.92

2.94 16.40

3 15.86

3.06 15.27

3.12 14.65


12/17

3.18 14.00

3.24 13.31

3.3 12.58

3.36 11.82

3.42 11.03

3.48 10.20

3.54 9.33

3.6 8.43

3.66 7.49

3.72 6.52

3.78 5.52

3.84 4.47

3.9 3.39

3.96 2.28

4.02 1.13

4.08 -0.05

4.14 -1.27

4.2 -2.52

4.26 -3.81

4.32 -5.14

4.38 -6.504.44 -7.90

4.5 -9.33

4.56 -10.79

4.62 -12.29

4.68 -13.83

4.74 -15.40

4.8 -17.01

4.86 -18.65


13/17

4.92 -20.33

4.98 -22.05

5.04 -23.79

5.1 -25.58

5.16 -27.40

5.22 -29.25

5.28 -31.14

5.34 -33.07

5.4 -35.03

5.46 -37.03

5.52 -39.06

5.58 -41.12

5.64 -43.23

5.7 -45.36

5.76 -47.54

5.82 -49.74

5.88 -51.99

5.94 -54.27

6 -56.58


14/17

velocity20.00 Plot of Velocity against Time

19.41

18.82

18.23

17.65

17.06

16.47

15.88

15.29

14.70

14.11

13.53

12.94

12.35

11.76

11.17 x-intercept = 2.039

10.58 This is where the velocity is equal to zero.

9.99

9.41 This is the same as the first difference on the "differences" tab.

8.82

8.23

7.64

7.05

6.46

y = -9.81x + 20

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

0 2 4 6 8

velocity

time


15/17

5.87

5.28

4.70

4.11

3.52

2.93

2.34

1.75

1.16

0.58

-0.01

-0.60

-1.19

-1.78

-2.37

-2.96

-3.54

-4.13

-4.72

-5.31

-5.90-6.49

-7.08

-7.66

-8.25

-8.84

-9.43

-10.02

-10.61


16/17

-11.20

-11.78

-12.37

-12.96

-13.55

-14.14

-14.73

-15.32

-15.90

-16.49

-17.08

-17.67

-18.26

-18.85

-19.44

-20.02

-20.61

-21.20

-21.79

-22.38

-22.97-23.56

-24.15

-24.73

-25.32

-25.91

-26.50

-27.09

-27.68


17/17

-28.27

-28.85

-29.44

-30.03

-30.62

-31.21

-31.80

-32.39

-32.97

-33.56

-34.15

-34.74

-35.33

-35.92

-36.51

-37.09

-37.68

-38.27

-38.86

contoh excel 2

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