แผน ค31102 -64

200

f x x 22 1 (2, 1)

a f
f2 1
41
15.
16.

y ax2 bx c, a 0

y = a x-h 2 k
(h, k)

y ax2 bx c

y x2 b x c
a aa
yc
aa x2 b x
y c b2 a
a a 4a2
y b2 4ac x2 bx b2
a 4a2 a 4a2
y
a x b2
2a
y
x b2 b2 4ac
y 2a 4a2

a x b 2 4ac b2
2a 4a

a x b 2 4ac b2
2a 4a

y = a x-h 2 k y ax2 bx c, a 0
f
b , 4ac b2 f(h) k
2a 4a

b , f b
2a 2a

17. 5

5 y x2 2x 8
x2 2x 8
y

a 1, b 2, c 8

201

b 21
2a 21
12 2 1 8
f b 9
2a (1, 9)

a0

(1, 9) 5

18.
19. 6

6 y 2x2 4x 16

y 2x2 4x 16

a 2, b 4, c 16

b 4 1 16 18
2a 22 41

fb 2 12
2a

( 1, 18)

a0

( 1, 18)

20. 6

7. (
8. 8
)

202
8

8 1. 8 -4
2. 60 %

8

-

-
-

-

203

8

(Quadratic function) a, b c

a0 y ax2 bx c
y 2x2 2x 1, y 7x2 4
a
a, b c

y ax2 bx c, a 0 y ax2 bx c, a 0

a0
a0

1 2) y 5x2 3) y 1 x2
1) y x2
5

204

2 x2 2) y 5x2 3) y 1 x2
1) y 5

205

3 3x2
1) y1
1 x
2) y2 2

3) y3 x 22 1
4) y4
x 22 1

206

4

1) f x x 22 1
2) f x x 22 1
3) f x x 22 1
4) f x x 22 1

207

5 y x2 2x 8

6 y 2x2 4x 16

208

8

1.

y ax2 bx c y a(x h)2 k, a 0

1) y x2 6x 4

2) y x2 4x 8

3) y 3x2 12x 3

4) y x2 2x 1

5) y x2 6x 4

2.
1)
2)
3)

1) f(x) x2 4x 7
2) f(x) 2x2 4x 3
3) f(x) 3x2 6x 3
4) f(x)
4x2 4x

209

8

1.

y ax2 bx c y a(x h)2 k, a 0

1) y x2 6x 4

y x2 6x 4

y x 32 9 4

x 3 2 13

(3, 13)

2) y x2 4x 8

y x2 4x 8
y x 22 4 8

x 22 4

(2, 4)

210

3) y 3x2 12x 3

y 3x2 12x 3
y 3 x2 4x 3

3 x 2 2 12 3
3 x 22 9

( 2, 9)

4) y x2 2x 1

y x2 2x 1
y x2 2x 1

x 12 1 1
x 12 2

(1, 2)

5) y x2 6x 4

y x2 6x 4
y x2 6x 4

x 32 9 4
x 3 2 13

211

( 3,13)

2.
1)
2)
3)

1) f(x) x2 4x 7
f(x) x2 4x 7

fx x 22 4 7
x 2 2 11

(2, 11)
x2

(2, 11)

Dr x x R
Rr y y 11

212

2) f(x) 2x2 4x 3
f(x) 2x2 4x 3
2 x2 2x 3
2 x 12 2 3
2 x 12 5

(1, 5)
x2

(1, 5)

3) f(x) Dr x x R
Rr y y 5

3x2 6x 3
f(x) 3x2 6x 3
3 x 2x 3
2 x 12 2 3
2 x 12 5

(1, 5)
x2

(1, 5)

213

Dr x x R
Rr y y 5

4) f(x) 4x2 4x

f(x) 4x2 4x
4 x2 x
4 x 12 1
2
1, 1
2
x2

1 , 1
2

1 , 1
2

Dr x x R
Rr y y 1

214

82

2 31102 4/4

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31102 2
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1.2
ax2 bx c 0 a0
4.1 y ax2 bx c

2

3
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:
1.
2.
3.
4.
5.

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1.

4
1.
2.

223
5

9

9
9

9

6. 9 9
9 9
-
3.
9
9

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. (2537).

. (2548). : . 224
. (2548) 4 2. :
(2548).
4 ( 4) :
2
. :

7.

-
-
-
-

ax2 bx c 0
y ax2 bx c

a0 X

25.

X

3.
4. 1

225

1 2x2 3 0
1

2x2 3 0 x 2x2 3
2x2 0

2x2 3 0

2

2x2 3 0 X
2x2 3 0 1

19. y a(x c)2 y a(x c)2 c0 2
20. 1

2

X ( c, 0) (c, 0)

y a(x c)2

a0

226

a0

5.
21. 2

2 3(x 2)2 0
1

3(x 2)2 0

3(x 2)2 0

(x 2)(x 2) 0

3(x 2)2 0
3(x 2)2
0 2

2 3(x 2)2 0

y 3(x 2)2

y0 x2

3(x 2)2 0 x2

3(x 2)2 0 2

22. 2 3
8.

227

3 y ax2 bx c, a 0 y y a(x h)2 k
y

23.
24. 3

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

0 x2
0

y 2(x 1)2 2

a 2, h 1 k2

a0 ( 1, 2)

y 2(x 1)2 2

y 2(x 1)2 2

y X (0, 0) ( 2, 0)
0
2(x 1)2 2 0 2
3
12.
13. 4

228

4 x2 9

1 y1 x2 y2 9 y1 y2

y1 y2 x 3 x3
3 3
x2 9

2 x2 9

x2 9 0 9
y x2

y

y x2 9 X y0

3, 0 3, 0 4

21. x2 9 33

9. X y a(x c)2 c0
2
y a(x c)2

X ( c, 0) (c, 0) 229
1
y a(x c)2
y a(x h)2 k
3 y ax2 bx c, a 0 y
(
y

10. 9
)

8

9 1. 9 9
2. 57

9

-
-
-

-

230

ax2 bx c 0

y ax2 bx c a0 X

( y 0)

12
34
56

231

1) 14 X

14

2) 2 5 X (n, 0) ( n, 0)

25

3) 3 6 X (p, 0) (q, 0)

36 2

X

1 2x2 3 0

232

2 3(x 2)2 0

3 2(x 1)2 2 0

233

4 x2 9

9 234

1) x2 1
2) 3x2 27
3) x2 8x 16 0
4) x2 1 0
5) (x 6)(x 4) 0

6) x2 2x 1 0
7) x2 3 0

9 235

1) x2 1 y

x2 1
x2 1 0
y x2 1

y X y0
11 1
( 1, 0) (1, 0)
x2

2) 3x2 27

3x2 27
x2 9 0

y x2 9

y

y X y0
33
( 3, 0) (3, 0) 27
3x2

236

3) x2 8x 16 0

x2 8x 16 0
y x2 8x 16

x 4 2 16 16
x 42

y x 42

x 42 y0 x4
0x 4
8x 16 0 4
x2

4) x2 1 0

x2 1 0
y x2 1
y x2 1

y x2 1 X

x2 1 0

237

5) (x 6)(x 4) 0

(x 6)(x 4) 0
y (x 6)(x 4)

x2 2x 24
x 1 2 1 24
x 1 2 25

y x 1 2 25

yX y0

( 4, 0) (6, 0) 6
(x 6)(x 4) 0
-4

6) x2 2x 1 0

x2 2x 1 0
y x2 2x 1
x2 2x 1
x 12 1 1
x 12

y x 12

238

y0 x1

x2 2x 1 0 x1
x2 2x 1 0
1

7) x2 30

x2 3 0

y x2 3
y x2 3

y x2 3 X
x2 3 0

239

9 2
11-12
2 31102 4/4

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1
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1. 200
1.2 X
x y0
4.1 x y0

2

1. y 0
2. ax2 bx c 0

X
3. ax2 bx c 0

X

3
:

:
1.
2.
3.
4.
5.

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4 248
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3). X x y0

4. ax2 bx c 0
5.
X

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