แผน ค31102 -64

250

1 x2 4

x2 4
x2 4 0

y x2 4

y x2 4

a 1, h 0 k 4
y x2 4
a0
y x2 4
0, 4

y x2 4

X
X y0

x2 4 0

(x 2)(x 2) 0

x2 x2

y x2 4 X 2, 0 2, 0

x y0 1

y0 2x2

x2 4 0 x2 4 2x2

25.
26. 2

2 0
1) x2 2x 3 0
2) x2 2x 3
a(x h)2 k
x2 2x 3

251

x2 2x 3 (x2 2x 1) 3 1
(x 1)2 4

a 1, h 1 k4

a0 y x2 2x 3

1, 4 y0

X

x2 2x 3 0
(x 3)(x 1) 0

x3 x1

y x2 2x 3 X 3, 0 1, 0

y x2 2x 3

y x2 2x 3

1) y 0 x2 2x 3 0 1x3
2) y 0 x2 2x 3 0 x 1 x3

27. 2
28. 3

3 x2 x 2 0

y x2 x 2

a0 y x2 x 2
y0
X

x2 x 2 0

x2 x 2 0
(x 2)(x 1) 0

252

x1 x2

y x2 x 2 X 1, 0 2, 0

y x2 x 2

y x2 x 2

y0 y0 1x2
x2 x 2 0 1x2

29. 3
30. 4

4
1) (x 1)(x 2) 0

2) x2 x 2
1) (x 1)(x 2) 0

x2 x 2 0

y x2 x 2

y x2 x 2

y x2

y y0

X

x2 x 2 0

(x 1)(x 2) 0

x1 x 2
y
X (1, 0) ( 2, 0)

y x2 x 2

253

y x2 x 2

x y0

y0 2x1

(x 1)(x 2) 0 2x1

2) x2 x 2 2
x2 y2 x
y1
y1 y2

y2 x 2

y1 x2

y1 y2 x1 x 2
y2
y1 y1 1 x 12
x1 y1 4
x2 y2 1
y1 y2 y2 4
( 1, 4)
(1, 1)

y2 x 2

y1 x2

y1 y2 x1 x1 254
(
y1 y2 x 1 x1

x1 x2 y1 y2

y1 y2 x2 x 2

x1 x1

31. 4

1.

1. y 0 X

2. ax2 bx c 0 x y0

X

3. ax2 bx c 0 x y0

X

2. 10

)

255
8

10 1. 10 10
2. 35

10

-

-
-

-

256

1

1. y 0 X
2. ax2 bx c 0 x y0

X x y0
3. ax2 bx c 0

X

1 x2 4

257

2
1) x2 2x 3 0
2) x2 2x 3 0

3 x2 x 2 0

258

4
1) (x 1)(x 2) 0
2) x2 x 2

259

10

1) x2 1 0
2) x2 7x 10 0
3) x2 2x
4) 2x 3 x 3

5) x2 6x 9 0

10 260

1) x2 1 y x2 1

x2 1
x2 1 0
y x2 1

X
X y0

x2 1 0

(x 1)(x 1) 0

x1 x1

y X ( 1, 0) (1, 0)
x1
x y0

y0 x1

x2 1 0 x2 1

x1 x1

2) x2 7x 10 0

x2 7x 10 0
y x2 7x 10
y x2 7x 10

261

X
X y0

x2 x5

y X (2, 0) (5, 0)

x y0

y0 2x5

x2 7x 10 0

2x5

3) x2 2x

x2 2x

x2 2x 0
(x2 2x) 0
(x 1)2 1 0

y (x 1)2 1

y

X
X y0

x0 x2

y X y0 (0, 0)
x0
x y0

y0 x2

x2 2x

x2 x0

262

4) 2x 3 x 3 0

2x 3 x 3 0

2x2 3x 9 0

y 2x2 3x 9 y

X

X y0

x3 x3
2

yX ( 3 , 0) (3, 0)
2

x y0

y0 3 x 3
2

2x 3 x 3 0 3x3
2

5) x2 6x 9 0

x2 6x 10 0

(x 3)2 0

y (x 3)2

y

263

X 3, 0
x y0
x3 x3
y0
x2 6x 10 0

x3 x3

264

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26. y ax a0 a1

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2

1. y ax a1 (0, 1) a0 1

275

2. a 1 x y
0a1 x y

a1 a 0, ax ay 0a1
xy
3. a 1
012
2. 1 124

1 y 2x y 2x

y 2x

x -2 -1

y 1 1
4 2

y 2x

xy y 2x
x y

x

276

3. 1
4.
2
2
y 1x
y 1x 2
2

x -2 -1 0 1 2

y 4 2 1 1 1
2 4

y 1x
2

x y
xy

5. 2
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277

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25
5x 1
25 x y(a 1, a 0)
x 2 5x 1
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52

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ax ay

x2

52 1 1
52 25

7. 3
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4x 1x1 16
4

1x1 16
4

16 42 12
4

1x1 12

44

ax ay x y(a 1, a 0)

x1 2

x3

x3 1x1 16
4

1 31 1 2 42 16
4 4

9. 4

1. y ax a0 a1

2. 11 ( )

278
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11 1. 11 11
2. 35

11

-

-
-

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279

11

y ax a0 a1

a 1 a1 y 1x 1

y 2x , y ex y 1x yx
2

1. y ax a1 (0, 1) a0 1

2. a 1 x y

0a1 x y

a1 a 0, ax ay 0a1
y 2x xy
3. a 1
1

280

2 y 1x

2

3x 5x 1
25

4x 1x1 16
4

281

11

1. 3) y 2 x
1) y 2 x 4) y 2x 1

2) y 3 x 1

2. x 2x 3 1
64

11 282

1.
1) y 2 x

y 2x

x -3 -2 -1 0 1 2 3

y 1 1 1 1 2 4 8
8 4 2

2) y 3 x 1

y 3x1

x -3 -2 -1 0 1 2 3

y 1 1 1 1 0 3 9
81 27 9 3

283

3) y 2 x

y 2x

x -3 -2 -1 0 1 2 3

y 1 1 1 1 2 4 8
8 4 2

4) y 2x 1

y 2x 1

x -3 -2 -1 0 1 2 3

y 7 3 1 0 1 3 7
8 4 2

284

2. x 2x 3 1
64

2x 3 1
64

11 24

64 24

2x 3 24

x3 4

x7

285

POWER POINT

y 2x , y ex y 1x yx
2

286

287

288

289

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