carpeta de trabajos (algebra ii)
DESCRIPTION
AlgebraTRANSCRIPT
Graficar las Sigs. Funciones.
F(x)= 2x+4
X Y
-5 -6
-4 -4
-3 -2
-2 0
1 6
2 8
3 10
4 12
5 14
F(x)= 3x-6
X Y
-5 -21
-4 -18
-3 -15
-2 -12
1 -3
2 0
3 3
4 6
5 9
F(x)= 2x+4 F(x)= 2x+4 F(x)= 2x+4 Y= 2(-5)+4 y= 2(-4)+4 y= 2(-3)+4 Y= -10+4 y= -8+4 y= -6+4 Y= -6 y= -4 y= -2
F(x)= 2x+4 F(x)= 2x+4 F(x)= 2x+4 Y= 2(-2)+4 y= 2(1)+4 y= 2(2)+4 Y= -4+4 y= 2+4 y= 4+4 Y= 0 y= 6 y= 8
F(x)= 2x+4 F(x)= 2x+4 F(x)= 2x+4 Y= 2(3)+4 y= 2(4)+4 y= 2(5)+4 Y= 6+4 y= 8+4 y= 10+4 Y= 10 y= 12 y= 14
F(x)= 3x-6 F(x)= 3x-6 F(x)= 3x-6 Y= 3(-5)-6 y= 3(-4)-6 y= 3(-3)-6 Y= -15+6 y= - 12-6 y= -9-6 Y= -21 y= -18 y= -15
F(x)= 3x-6 F(x)=3x-6 F(x)= 3x-6 Y= 3(-2)-6 y= 3(1)-6 y= 3(2)-6 Y= -6-6 y= 3-6 y= 6-6 Y= -12 y= -3 y= 0
F(x)= 3x-6 F(x)= 3x-6 F(x)= 3x-6 Y= 3(3)-6 y= 3(4)-6 y= 3(5)-6 Y= 9-6 y= 12-6 y= 15-6 Y= 3 y= 6 y= 9
Y= 3x-1
X Y
-5 -16
-4 -13
-3 -10
-2 -7
1 2
2 5
3 8
4 11
5 14
F(x)= 2x2+4
X Y
-5 54
-4 36
-3 22
-2 12
1 6
2 12
3 22
4 36
5 54
Y= 3x-1 Y= 3x-1 Y= 3x-1 Y= 3(-5)-1 y= 3(-4)-1 y= 3(-3)-1 Y= -15-1 y= - 12-1 y= -9-1 Y= -16 y= -13 y= -10
Y= 3x-1 Y= 3x-1 Y= 3x-1 Y= 3(-2)-1 y= 3(1)-1 y= 3(2)-1 Y= -6-1 y= 3-1 y= 6-1 Y= -7 y= 2 y= 5
Y= 3x-1 Y= 3x-1 Y= 3x-1 Y= 3(3)-1 y= 3(4)-1 y= 3(5)-1 Y= 9-1 y= 12-1 y= 15-1 Y= 8 y= 11 y= 14
F(x)= 2x2+4 F(x)= 2x2+4 F(x)= 2x2+4 Y= 2(-5)2+4 y= 2(-4)2+4 y= 2(-3)2+4 Y= 50+4 y= 32+4 y= 18+4 Y= 54 y= 36 y= 22
F(x)= 2x2+4 F(x)= 2x2+4 F(x)= 2x2+4 Y= 2(-2)2+4 y= 2(1)2+4 y= 2(2)2+4 Y= 8+4 y= 2+4 y= 8+4 Y= 12 y= 6 y=12
F(x)= 2x2+4 F(x)= 2x2+4 F(x)= 2x2+4 Y= 2(3)2+4 y= 2(4)2+4 y= 2(5)2+4 Y= 18+4 y= 32+4 y= 50 Y= 22 y= 36 y= 54
F(x)= 3x2-6
X Y
-5 69
-4 42
-3 21
-2 6
1 -3
2 6
3 21
4 42
5 69
Y= 3x2-1
X Y
-5 74
-4 47
-3 26
-2 11
1 2
2 11
3 26
4 47
5 74
F(x)= 3x2-6 F(x)= 3x2-6 F(x)= 3x2-6 Y= 3(-5)2-6 y= 3(-4)2-6 y= 3(-3)2-6 Y= 75-6 y= 48-6 y= 27-6 Y= 69 y= 42 y= 21
F(x)= 3x2-6 F(x)= 3x2-6 F(x)= 3x2-6 Y= 3(-2)2-6 y= 3(1)2-6 y= 3(2)2-6 Y= 12-6 y= 3-6 y= 12-6 Y= 6 y= -3 y= 6
F(x)= 3x2-6 F(x)= 3x2-6 F(x)= 3x2-6 Y= 3(3)2-6 y= 3(4)2-6 y= 3(5)2-6 Y= 27-6 y= 48-6 y= 75-6 Y= 21 y= 42 y= 69
Y= 3x2-1 Y= 3x2-1 Y= 3x2-1 Y= 3(-5)2-1 y= 3(-4)2-1 y= 3(-3)2-1 Y= 75-1 y= 48-1 y= 27-1 Y= 74 y= 47 y= 26
Y= 3x2-1 Y= 3x2-1 Y= 3x2-1 Y= 3(-2)2-1 y= 3(1)2-1 y= 3(2)2-1 Y= 12-1 y= 3-1 y= 12-1 Y= 11 y= 2 y= 11
Y= 3x2-1 Y= 3x2-1 Y= 3x2-1 Y= 3(3)2-1 y= 3(4)2-1 y= 3(5)2-1 Y= 27-1 y= 48-1 y= 75-1 Y= 26 y= 47 y= 74
1.- F(x)= 2x2+3x-2
X Y
-3 7
-2 0
-1 -3
0 -2
1 3
2 12
3 25
2.- F(x)= -x2+5x-8
X Y
-3 -14
-2 -14
-1 -12
0 -8
1 -4
2 -2
3 -2
F(x)= 2x2+3x-2 F(x)= 2x2+3x-2 F(x)= 2x2+3x-2 Y= 2(-3)2+3(-3)-2 Y= 2(-2)2+3(-2)-2 Y= 2(-1)2+3(-1)-2 Y= 18-9-2 Y= 8-6-2 Y= 2-3-2 Y= 18-11 Y= 8-8 Y= 2-5 Y= 7 Y= 0 Y= -3
F(x)= 2x2+3x-2 F(x)= 2x2+3x-2 F(x)= 2x2+3x-2 Y= 2(0)2+3(0)-2 Y= 2(1)2+3(1)-2 Y= 2(2)2+3(2)-2 Y= 0+0-2 Y= 2+3-2 Y= 8+6-2 Y= -2 Y= 3 Y= 12
F(x)= 2x2+3x-2 Y= 2(3)2+3(3)-2 Y= 18+9-2 Y= 25
F(x)= -x2+5x-8 F(x)= -x2+5x-8 F(x)= -x2+5x-8 Y= -(-3)2+5(-3)-8 Y= -(-2)2+5(-2)-8 Y= -(-1)2+5(-1)-8 Y= 9-15-8 Y= 4-10-8 Y= 1-5-8 Y= 9-23 Y= 4-18 Y= 1-13 Y= -14 Y= -14 Y= -12
F(x)= -x2+5x-8 F(x)= -x2+5x-8 F(x)= -x2+5x-8 Y= -(0)2+5(0)-8 Y= -(1)2+5(1)-8 Y= -(2)2+5(2)-8 Y= 0+0-8 Y= -1+5-8 Y= -4+10-8 Y= -8 Y= -1-3 Y= -4+2
Y= -4 Y= -2
F(x)= -x2+5x-8 Y= -(3)2+5(3)-8 Y= -9+15-8 Y= -9+7 Y= -2
3.- Y= x2+6x+5
X Y
-3 -4
-2 -3
-1 0
0 5
1 12
2 21
3 32
4.- Y= x2+5x+10
X Y
-3 4
-2 4
-1 6
0 10
1 16
2 24
3 34
Y= x2+6x+5 Y= x2+6x+5 Y= x2+6x+5 Y= (-3)2+6(-3)+5 Y= (-2)2+6(-2)+5 Y= (-1)2+6(-1)+5 Y= 9-18+5 Y= 4-12+5 Y= 1-6+5 Y= 9-13 Y= 4-7 Y= 1-1 Y= -4 Y= -3 Y= 0
Y= x2+6x+5 Y= x2+6x+5 Y= x2+6x+5 Y= (0)2+6(0)+5 Y= (1)2+6(1)+5 Y= (2)2+6(2)+5 Y= 0+0+5 Y= 1+6+5 Y= 4+12+5 Y= 5 Y= 1+11 Y= 4+17
Y= 12 Y= 21
Y= x2+6x+5 Y= (3)2+6(3)+5 Y= 9+18+5 Y= 9+23 Y= 32
Y= x2+5x+10 Y= x2+5x+10 Y= x2+5x+10 Y= (-3)2+5(-3)+10 Y= (-2)2+5(-2)+10 Y= (-1)2+5(-1)+10 Y= 9-15+10 Y= 4-10+10 Y= 1-5+10 Y= 9-5 Y= 4+0 Y= 1+5 Y= 4 Y= 4 Y= 6
Y= x2+5x+10 Y= x2+5x+10 Y= x2+5x+10 Y= (0)2+5(0)+10 Y= (1)2+5(1)+10 Y= (2)2+5(2)+10 Y= 0+0+10 Y= 1+5+10 Y= 4+10+10 Y= 10 Y= 1+15 Y= 4+20
Y= 16 Y= 24
Y= x2+5x+10 Y= (3)2+5(3)+10 Y= 9+15+10 Y= 9+25 Y= 34
5.- 2y= 4x2+8x+4
X Y
-3 8
-2 2
-1 0
0 2
1 8
2 18
3 32
2y= 4x2+8x+4 2y= 4x2+8x+4 2y= 4x2+8x+4 2y= 4(-3)2+8(-3)+4 2y= 4(-2)2+8(-2)+4 2y= 4(-1)2+8(-1)+4 2y= 4(9)-24+4 2y= 4(4)-16+4 2y= 4(1)-8+4 2y= 36-24+4 2y= 16-16+4 2y= 4-8+4 2y= 12+4 2y= 4 2y= 0 2y= 16 y= 4/2 y= 0/2 y= 16/2 y= 2 y= 0 y= 8
2y= 4x2+8x+4 2y= 4x2+8x+4 2y= 4x2+8x+4 2y= 4(0)2+8(0)+4 2y= 4(1)2+8(1)+4 2y= 4(2)2+8(2)+4 2y= 0+0+4 2y= 4(1)+8+4 2y= 4(4)+16+4 2y= 4 2y= 4+8+4 2y= 16+16+4 y= 4/2 2y= 16 2y= 36 y= 2 y= 16/2 y= 36/2
y= 8 y= 18
2y= 4x2+8x+4 2y= 4(3)2+8(3)+4 2y= 4(9)+24+4 2y= 36+24+4 2y= 64 y= 64/2 y= 32
F(x)= 2x+1
X Y
-2 -3
-1 -1
0 1
1 3
2 5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-4
-3
-2
-1
0
1
2
3
4
5
6
y
y
F(x)= 2x+1 F(x)= 2x+1
y= 2x+1 y= 2(-1)+1
y= 2(1)+1 y= -2+1
y= 2+1 y= -1
F(x)= 4x-1
X Y
-2 -9
-1 -5
0 -1
1 3
2 7
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-10
-8
-6
-4
-2
0
2
4
6
8
y
y
X Y
F(x)= 4x-1 F(x)= 4x-1 F(x)= 4x-1
y= 4(-2)-1 y= 4(-1)-1 y= 4(0)-1
y= -8-1 y= -4-1 y= 0-1
y= -9 y= -5 y= -1
F(x)= 4x-1 F(x)= 4x-1
A) (3,-2)B) (-4,2)
-5 -4 -3 -2 -1 0 1 2 3 4
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
y
y
X YA) (-2,0)B) (4,8)
-3 -2 -1 0 1 2 3 4 50
1
2
3
4
5
6
7
8
9
Y
Y
1) 3x-5= y
2) 4x-2y=4
X Y
-2 -11
-1 -8
0 -5
1 -2
2 1
4x-2y=4
X Y
0 -2
1 0
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-12
-10
-8
-6
-4
-2
0
2
y
y
X Y
Y= 3x-5 Y= 3x-5 Y= 3x-5 y= 3(-2)-5 y= 3(-1)-5 y= 3(0)-5 y= -6-5 y= -3-5 y= 0-5 y= -11 y= -8 y= -5
Y= 3x-5 Y= 3x-5 y= 3(1)-5 y= 3(2)-5 y= 3-5 y= 6-5 y= -2 y= 1
-2y=4-4x y4−4 (1)
−2= y= 4−4 (2)
−2
Y= 4−4 x−2 y=
4−4−2
Y= 4−4 (0)
−2 y=
0−2
Y=4−0−2 y= 0
Y= 4/-2= -2
-1 1
0 4
1 7
Y= 3(-1)+4 y= 3(0)+4 y= 3(1)+4Y= -3+4 y= 0+4 y= 3+4Y= 1 y= 4 y= 7
-1.5 -1 -0.5 0 0.5 1 1.5012345678
y
y
X Y
-1 -3
-5 -6
Y= 9−3 x−4
Y= 9−3 (−1)
−4= =
9+3−4 =
12−4 = -3
Y= 9−3 (−5)
−4 = 9+15−4 =
24−4 = -6
-5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5
-7-6-5-4-3-2-10
Y
Y
X Y
1 -0.6
0 0
-1 0.6
Y= −23x
Y= -0.6xY= -0.6(1)= -0.6Y= -0.6(0)= 0Y= -0.6(-1)= 0.6
X Y
1 -2.3
-2 -4.3
Y= −57x−3
Y= 0.7x-3= 0.7(1)-3= -2.3Y= 0.7x-3=0.7(-2)-3= -4.3
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Y
Y
-1.5 -1 -0.5 0 0.5 1 1.5
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Y
Y
Y= 5x-7
X Y
-1 -12
1 -2
Y= 5(-1)-7Y= -5-7Y= -12
y= 5(1)-7y= 5-7y= -2
2x-y=-4
X Y
-1 -2
1 -6
-Y= -4-2x -y= -4-2(1)-y= -4-2(-1) -y= -4-2-y= -4+2 -y= -6-y= -2
-1.5 -1 -0.5 0 0.5 1 1.5
-7
-6
-5
-4
-3
-2
-1
0
Y
Y
-1.5 -1 -0.5 0 0.5 1 1.5
-14
-12
-10
-8
-6
-4
-2
0
Y
Y
X Y
-1 2.5
-2 4
3x+2y=2 2y= 2-3x2y= 2-3x 2y= 2-3(-2)2y= 2-3(-1) 2y= 2+62y= 2+3 2y= 82y= 5 y= 8/2 Y= 5/2 y= 4 Y= 2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-3
-2
-1
0
1
2
3
4
5
Y
Y
X Y
-1 7
1 3
2x-y=5-y= 5-2x-y= 5-2(-1)-y= 5+2-y= 7
-y= 5-2x-y= 5-2(1)-y= 5-2-y= 3
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-2
-1
0
1
2
3
4
5
6
7
8
Y
Y
X Y
-1 2.4
1 1.6
2x+5y=10
Y= 10−2 x5
y= 10−2(1)
5
Y=10−2(−1)
5 y=
10−25
Y= 10+25
y= 8/5
Y= 12/5 y= 1.6
Y= 2.4
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
Y
Y
1) 2x+8=3
X= −8+32
21
(- 52
)+8=3
X= −52
-102
+8=3
X= -2.5 -5+8=3 3=3
2) 9x+6=2x(3) 9(-2)+6=2(-2)(3)9x +6=6x -18+6=-129x-6x=-6 12=-123x=-6
X= - 63
X= -2
3)12
x+34
=85
10x+15=3220
=x=32-15=1710
4) X+12
x=2x+13
11
x+12
x=21
x+13
=6 x+3 x=12 x+2
6=9 x−12x=2
6=3x=26
=x=23
5) 6x(x+3)-2=3x(2x-1)6x2+18x-2=6x2-3x6x2+18x-6x2+3x=221x=2X=2/21
6) 9x(x-6)-16=3x(2x+4)+3x(x-6)9x2-54x-16=6x2+12x+3x2-18x9x2-324x-6x2-12x-3x2+18x0+330xX= -330
7)x+23
=2x−34
2x3
=−1x4
=8 x−3 x24
=5x24
=x=524
8)12
x(x+1)=23
(x+1)+12
x+8
12
x2+12
x=23
x+23
+12
x+8
12
x2+12
x=76
x+263
12
x2+12
x-76
x=263
12
x2-23
x=263
12
x2-23
x-263
=0
−(−23
)±√(−23 )2
−41 ( 12 )(−263 )
2( 12)
23±√ 49❑
+ 1046
1
23±√ 24+93654
❑
1
23±√ 96054 ❑
1
23±√17
1
X= 23±4.1
X1=23+4
1x2=
23−4
1
X1= 14 x2= −103
1) 20=x3
-10 20=−903
-10
x3
=-10-20−903
= -10-20
x3= -30 -30= -30 Q.E.D.
X=-30(3) X= -90
2) 20=3X-10 20=3(10)-10-3X=-20-10 20=30-10-3X= -30 20=20 Q.E.D
X= - -303
X= 10
3) 15=34
y
-- 34
y= -15 20=34
(201
)
Y= −15
−0.75 20=80+34
=834
Y= 20 20=20 Q.E.D.
4) 17=24-22=24-17 17=24-72= -7 17=17 Q.E.D.
5) 3=39X
3= 3936
X=39-3 36=39-3X=36 36=36 Q.E.D.
6)15x
=54
X= (54
) ( 151
)= 754
151754
= 54
Q.E.D.
X= 754
7) 5c=2c+4.5-2c+5c=4.5 5(1.5)=2(1.5)+4.53c=4.5 -2(1.5)+5(1.5)=4.5C= 4.5/3 -3.0+7.5=4.5C= 1.5 4.5=4.5 Q.E.D.
8)34
n+1112
=2012
34
n= 2012
-1112
34
(12)+1112
=2012
0.75n=9 0.75(12)+1112
=2012
N= 90.75
9+1112
=2012
N= 12 2012
=2012
9) x2
+ 27=3062
+27=30
X= 30-27(2) 6= 30-27(2)X= 3(2) 6=3(2)X= 6 6=6 Q.E.D.
10) 8x+3=43
X= 43−38
8(5)+3=43
X= 408
40=43-3
X= 5 40=40 Q.E.D.
11) 21= 75
w
−75
w = -21 21= 75
(15)
-1.4w = −21−1.4 21=1.4(15)
w=15 21=21 Q.E.D.
12) 60=66-12w-12w= 66-60 60= 66-12(-0.5)-12w= 6 -12(-0.5)=66-60
w= 6
−12 -12(-0.5)=6
w= -0.5 6 = 6 Q.E.D.
13) 10b-3b=497b=49 10(7)-3(7)= 49b= 49/7 70-21= 49b= 7 49=49 Q.E.D.
14) 12b-5=0.28+b12b-b=0.28+5 12(0.48)-5= 0.28+0.4811b= 5.28 5.76-5= 0.28+0.48
b= 5.2811
5.76-0.48= 5+0.28
b= 0.48 5.28=5.28 Q.E.D.
15) 40-35
m= 37
- 35
m= 37-40 40- 35
(5)=37
-0.6m = -3 - 35
(5)= 37-40
m= -3/0.6 -0.6(5)=-3m= 5 -3= -3 Q.E.D.
34
n +1112
= 2012
34
n + 232
= 412
34
(121
)+1112
=2012
34
n = 412
- 232
364
+ 23−2 =
412
34
n= 182
n= 182
34
n= 726
=363
=12
1) 5(x+3)-2x=3(2x-1) 5x+15-2x=6x-3 5x-2x-6x= -3-15
-3x= -18
X= −18−3
X= 6
2) 6a-1+3(a+6)= 2 6a-1+3a+18= 2 6a+3a= 2+17
9a= 19a= 19/9a= 2.1
Graficar Tabular Ecuación Formula
1)F(x)= 2x2-8x-24 Ax2+Bx+c=0 −b±√b2−4 ac2a
2x2-8x+24=0
x 2x2-8x-24-4 40-3 18-2 0-1 -140 -241 -302 -323 -304 -245 -146 07 188 40
Y= 2(-4)2-8(-4)-24 y= 2(-3)2-8(-3)-24 y= 2(-2)2-8(-2)-24Y= 32+32-24 y= 18+24-24 y= 8+16-24Y= 64-24 y= 42-24 y= 24-24Y= 40 y= 18 y= 0
Y= 2(-1)2-8(-1)-24 y= 2(0)2-8(0)-24 y= 2(1)2-8(1)-24Y= 2+8-24 y= 0-0-24 y= 2-8-24Y= 10-24 y= -24 y= -6-24Y= -14 y= -30
Y= 2(2)2-8(2)-24 y= 2(3)2-8(3)-24 y= 2(4)2-8(4)-24Y= 8-16-24 y= 18-24-24 y= 32-32-24Y= -8-24 y= -6-24 y= 0-24Y= -32 y= -30 y= -24
Y= 2(5)2-8(5)-24 y= 2(6)2-8(6)-24 y= 2(7)2-8(7)-24Y= 50-40-24 y= 72-48-24 y= 98-56-24Y= 10-24 y= 24-24 y= 42-24Y= -14 y= 0 y= 18
Y= 2(8)2-8(8)-24Y= 128-64-24Y= 64-24Y= 40
1) 2x2-8x+24=0 −b±√b2−4 ac2a
A= 2
B= -8−(−8)±√(−8)2−4 (2 )(−24)
2(2)C= -24
X= 8±√64+192
4x= 8±2 x2=
8−24
X= 8±√2564
x1= 8+24
x2= 1.5
X= 8±√164
x1= 2.5
X= 8±√44
2) 3x2-5x-2=0 −b±√b2−4 ac2a
A= 3
B= -5−(−5)±√(−5)2−4 (3 )(−2)
2(3)C= -2
X= 5±√25+24
6X= 5±0.1 x2=
5−0.16
X= 5±√496
x1= 5+0.16
x2= 0.81
X= 5±√76
x1= 0.85
X= 5±√1.16
Graficar Tabular Ecuación Formula
2)F(x)= 3x2-5x-2 Ax2+Bx+c=0 −b±√b2−4 ac2a
3x2-5x-2=0
x 2x2-8x-24-4 66-3 40-2 20-1 60 -21 -42 03 104 265 486 767 1108 150
Y= 3(-4)2-5(-4)-2 y= 3(-3)2-5(-3)-2 y= 3(-2)2-5(-2)-2Y= 48+20-2 y= 27+15-2 y= 12+10-2Y= 68-2 y= 42-2 y= 22-2Y= 66 y= 40 y= 20
Y= 3(-1)2-5(-1)-2 y= 3(0)2-5(0)-2 y= 3(1)2-5(1)-2Y= 3+5-2 y= 0-0-2 y= 3-5-2Y= 8-2 y= -2 y= -2-2Y= 6 y= -4
Y= 2(2)2-8(2)-24 y= 2(3)2-8(3)-24 y= 2(4)2-8(4)-24Y= 8-16-24 y= 18-24-24 y= 32-32-24Y= -8-24 y= -6-24 y= 0-24Y= -32 y= -30 y= -24
Y= 2(5)2-8(5)-24 y= 2(6)2-8(6)-24 y= 2(7)2-8(7)-24Y= 50-40-24 y= 72-48-24 y= 98-56-24Y= 10-24 y= 24-24 y= 42-24Y= -14 y= 0 y= 18
Y= 2(8)2-8(8)-24Y= 128-64-24Y= 64-24Y= 40
Graficar Tabular Ecuación Formula
3)F(x)= x2 Ax2+Bx+c=0 X=b±√b2−4 a2a
x x2
-4 66-3 40-2 20-1 60 -21 -42 03 104 265 486 767 1108 150
Y= (-4)2 Y=(-3)2 Y=(-2)2 Y=(-1)2 Y=(0)2 Y=(1)2 Y=(2)2
Y= 16 Y= 9 Y= 4 Y= 1 Y= 0 Y= 1 Y= 4
Y= (3)2 Y=(4 )2 Y=(5 )2 Y=(6 )2 Y=(7 )2 Y=(8 )2
Y= 9 Y= 16 Y= 25 Y= 36 Y= 49 Y= 64
Graficar Tabular Ecuación Formula
4)F(x)=2(X-2)2 Ax2+Bx+c=0 −b±√b2−4 ac2a
2x2-8x+8=0
x 2x2-8x-24-4 66-3 40-2 20-1 60 -21 -42 03 104 265 486 767 1108 150
Y=2(-4)2-8(-4)+8 y= 2(-3)2-8(-3)+8 y= 2(-2)2-8(-2)+8Y= 32+32+8 y= 18+24-8 y= 8+16+8Y= 64+8 y= 42+8 y= 24+8Y= 72 y= 50 y= 32
Y= 2(-1)2-8(-1)+8 y= 2(0)2-8(0)+8 y= 2(1)2-8(1)+8Y= 2+8+8 y= 0-0+8 y= 2-8+8Y= 10+8 y= 8 y= -6+8Y= 18 y= 2
Y= 2(2)2-8(2)+8 y= 2(3)2-8(3)+8 y= 2(4)2-8(4)+8Y= 8-16+8 y= 18-24+8 y= 32-32+8Y= -8+24 y= -6+8 y= 8Y= 0 y= 2
Y= 2(5)2-8(5)+8 y= 2(6)2-8(6)+8 y= 2(7)2-8(7)+8Y= 50-40+8 y= 72-48+8 y= 98-56+8Y= 10+8 y= 24+8 y= 42+8Y= 18 y= 32 y= 50
Y= 2(8)2-8(8)+8Y= 128-64+8Y= 64+8Y= 72
4) 2x2-8x+8 −b±√b2−4 ac2a
A= 2
B= -8−(−8)±√(−8)2−4 (2 )(8)
2(2)
C= 8
X= 8±√64+64
4x= 8±0 x2=
8−04
X= 8±√04
x1= 8+04
x2= 2
X= 8±√04
x1= 2
X= 8±√04
5) 2x2-8x+2 x=−b±√b2−4ac2a
A= 3
B= -5 x=−(−8)±√(−8)2−4 (2 )(2)
2(2)C= -2
X= 8±√64+16
4X= 8±0.4 x2=
8−0.44
X= 8±√484
x1= 8+0.44
x2= 1.9
X= 8±√6.94
x1= 2.1
X= 8±√1.74
Graficar Tabular Ecuación Formula
4)F(x)=2(X-2)2 Ax2+Bx+c=0 −b±√b2−4 ac2a
2x2-8x+8=0
Y=2(-4)2-8(-4)+8 y= 2(-3)2-8(-3)+8 y= 2(-2)2-8(-2)+8Y= 32+32+8 y= 18+24-8 y= 8+16+8Y= 64+8 y= 42+8 y= 24+8Y= 72 y= 50 y= 32
Y= 2(-1)2-8(-1)+8 y= 2(0)2-8(0)+8 y= 2(1)2-8(1)+8Y= 2+8+8 y= 0-0+8 y= 2-8+8Y= 10+8 y= 8 y= -6+8Y= 18 y= 2
Y= 2(2)2-8(2)+8 y= 2(3)2-8(3)+8 y= 2(4)2-8(4)+8Y= 8-16+8 y= 18-24+8 y= 32-32+8Y= -8+24 y= -6+8 y= 8Y= 0 y= 2
Y= 2(5)2-8(5)+8 y= 2(6)2-8(6)+8 y= 2(7)2-8(7)+8Y= 50-40+8 y= 72-48+8 y= 98-56+8Y= 10+8 y= 24+8 y= 42+8Y= 18 y= 32 y= 50
Y= 2(8)2-8(8)+8Y= 128-64+8Y= 64+8Y= 72
x 2x2-8x-24-4 66-3 40-2 20-1 60 -21 -42 03 104 265 486 767 1108 150
Graficar Tabular Ecuación Formula
5)F(x)=2(X-2)2-6 Ax2+Bx+c=0 −b±√b2−4 ac2a
2x2-8x+8=0X2+4x+42(x2-4x+4)2 x2+8x+8-62 x2-8x+2
Y=2(-4)2-8(-4)+8 y= 2(-3)2-8(-3)+8 y= 2(-2)2-8(-2)+8Y= 32+32+8 y= 18+24-8 y= 8+16+8Y= 64+8 y= 42+8 y= 24+8Y= 72 y= 50 y= 32
Y= 2(-1)2-8(-1)+8 y= 2(0)2-8(0)+8 y= 2(1)2-8(1)+8Y= 2+8+8 y= 0-0+8 y= 2-8+8Y= 10+8 y= 8 y= -6+8Y= 18 y= 2
Y= 2(2)2-8(2)+8 y= 2(3)2-8(3)+8 y= 2(4)2-8(4)+8Y= 8-16+8 y= 18-24+8 y= 32-32+8Y= -8+24 y= -6+8 y= 8Y= 0 y= 2
Y= 2(5)2-8(5)+8 y= 2(6)2-8(6)+8 y= 2(7)2-8(7)+8Y= 50-40+8 y= 72-48+8 y= 98-56+8Y= 10+8 y= 24+8 y= 42+8Y= 18 y= 32 y= 50
Y= 2(8)2-8(8)+8Y= 128-64+8Y= 64+8Y= 72
x 2x2-8x-24-4 66-3 44-2 26-1 120 21 42 -63 -44 25 126 267 448 66
