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Anexos:
Anônimo:
f(x) = 2x² + 2x - 1 ?
Respostas
respondido por:
1
1) f(0) = 0+0-1 = -1
f(1) =2+2-1 = 3
f(1/3)=2.1/9+3/3-1 //tira o mmc de 9 e 3 q é 9 //
2+6-9/9 =-1/9
2)
f(2)=2²-3.2+2 f(-3)=(-3)²-(3*-3)+2 f(0)=0²+3.0+2
f(2)=4-6+2 f(-3)=9+9+2 f(0)=2
f(2)=0 f(-3)=20
0+20/2 =10
3)
a)
x²-4x+3
delta=b² - 4*a*c
delta=16-4.1.3
delta=16-12
delta=4
x= -b +/- 2/2*a
x1=-(-4)+2/2 x2=-(-4)-2/2
x1=4+2/2 x2=4-2/2
x1=3 x2=1
b)2x²-2x-4
delta=4-4*2*(-4)
delta=36
x1=2+6/4 x2=2-6/4
x1=2 x2=-1
d)x²+3x+2
delta=9-4*1*2
delta=1
x1=-3+1/2 x2=-3-1/2
x1=-1 x2=-2
e)x²-4x+4
delta=16-4.1.4
delta=0
x=-(-4)/2
x=2
f(1) =2+2-1 = 3
f(1/3)=2.1/9+3/3-1 //tira o mmc de 9 e 3 q é 9 //
2+6-9/9 =-1/9
2)
f(2)=2²-3.2+2 f(-3)=(-3)²-(3*-3)+2 f(0)=0²+3.0+2
f(2)=4-6+2 f(-3)=9+9+2 f(0)=2
f(2)=0 f(-3)=20
0+20/2 =10
3)
a)
x²-4x+3
delta=b² - 4*a*c
delta=16-4.1.3
delta=16-12
delta=4
x= -b +/- 2/2*a
x1=-(-4)+2/2 x2=-(-4)-2/2
x1=4+2/2 x2=4-2/2
x1=3 x2=1
b)2x²-2x-4
delta=4-4*2*(-4)
delta=36
x1=2+6/4 x2=2-6/4
x1=2 x2=-1
d)x²+3x+2
delta=9-4*1*2
delta=1
x1=-3+1/2 x2=-3-1/2
x1=-1 x2=-2
e)x²-4x+4
delta=16-4.1.4
delta=0
x=-(-4)/2
x=2
respondido por:
0
1.
a)
f(x) = 2x² + 2x - 1
f(-1) = 2.(-1)² + 2.(-1) - 1
f(-1) = 2.1 - 2 - 1
f(-1) = 2 - 2 - 1
f(-1) = - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
f(x) = 2x² + 2x - 1
f(2) = 2.2² + 2.2 - 1
f(2) = 2.4 + 4 - 1
f(2) = 8 + 3
f(2) = 11
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
f(x) = 2x² + 2x - 1
f(3) = 2.3² + 2.3 - 1
f(3) = 2.9 + 6 - 1
f(3) = 18 + 5
f(3) = 23
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
f(x) = 2x² + 2x - 1
f(-2) = 2.(-2)² + 2.(-2) - 1
f(-2) = 2.4 - 4 - 1
f(-2) = 8 - 5
f(-2) = 3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
f(x) = 2x² + 2x - 1
f(0) = 2.0² + 2.0 - 1
f(0) = - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
f)
f(x) = 2x² + 2x - 1
f(1) = 2.1² + 2.1 - 1
f(1) = 2.1 + 2 - 1
f(1) = 2 + 2 - 1
f(1) = 4 - 1
f(1) = 3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
f(1/3) = 2.(1/3)² + 2.1/3 - 1
f ( 1) = 2 . 1² + 2. 1 - 1
----- ------ -----
( 3) 3² 3
f(1/3) = 2. 1 + 2 - 1
----- -----
9 3
f(1/3) = 2 + 2 - 1
------ -----
9 3
2 + 6 - 9 8 - 9 - 1
f(1/3) = --------------- = ----------- = ------
9 9 9
**************************************
2.
f(x) = x² - 3x + 2
f(2) = 2² - 3.2 + 2
f(2) = 4 - 6 + 2
f(2) = 4 + 2 - 6
f(2) = 6 - 6
f(2) = 0
f(x) = x² - 3x + 2
f(-3) = (-3)² - 3.(-3) + 2
f(-3) = 9 + 9 + 2
f(-3) = 18 + 2
f(-3) = 20
f(x) = x² - 3x + 2
f(0) = 0² - 3.0 + 2
f(0) = 2
f(2) + f(-3) = 0 + 20
----------------- ----------- = 20/2 = 10
f(0) 2
*****************************************
3.
a)
f(x) = x² - 4x + 3
0 = x² - 4x + 3
x² - 4x + 3 = 0
a = 1; b = - 4; c = 3
Δ = b² - 4ac
Δ = (-4)² - 4.1.3
Δ = 16 - 12
Δ = 4
x = - b +/- √Δ = - ( - 4) +/- √4
-------------- ---------------------
2a 2.1
x = 4 + 2
--------- = 6/2 = 3
2
x = 4 - 2 = 2/2 = 1
--------
2
***********************************
b)
f(x) = 2x² - 2x - 4
0 = 2x² - 2x - 4
2x² - 2x - 4 = 0 (:2)
x² - x - 2 = 0
a = 1; b = - 1; c = - 2
Δ = b² - 4ac
Δ = (-1)² - 4.1.(-2)
Δ = 1 + 8
Δ = 9
x = - b +/- √Δ = - (-1) +/- √9
--------------- ------------------
2a 2.1
x = 1 + 3
---------- = 4/2 = 2
2
x = 1 - 3 = - 2/2 = - 1
---------
2
*****************************************
c)
f(x) = x² - 9
0 = x² - 9
9 = x²
x² = 9
x = √9
x = 3 e x = - 3
*****************************************
d)
f(x) = x² + 3x + 2
0 = x² + 3x + 2
x² + 3x + 2 = 0
a = 1; b = 3; c = 2
Δ = b² - 4ac
Δ = 3² - 4.1.2
Δ = 9 - 8
Δ = 1
x = - b +/- √Δ = - 3 +/- √1
------------- -------------------
2a 2.1
x = - 3 + 1
---------- = - 2/2 = - 1
2
x = - 3 - 1 = -4/2 = - 2
----------
2
****************************************
e)
f(x) = x² - 4x + 4
0 = x² - 4x + 4
x² - 4x + 4 = 0
a = 1; b = - 4; c = 4
Δ = b² - 4ac
Δ = (-4)² - 4.1.4
Δ = 16 - 16
Δ = 0 (uma raiz)
x = - b +/- √Δ = - (-4) +/- √0
---------------- -----------------
2a 2.1
x = 4/2
x = 2
a)
f(x) = 2x² + 2x - 1
f(-1) = 2.(-1)² + 2.(-1) - 1
f(-1) = 2.1 - 2 - 1
f(-1) = 2 - 2 - 1
f(-1) = - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
f(x) = 2x² + 2x - 1
f(2) = 2.2² + 2.2 - 1
f(2) = 2.4 + 4 - 1
f(2) = 8 + 3
f(2) = 11
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
f(x) = 2x² + 2x - 1
f(3) = 2.3² + 2.3 - 1
f(3) = 2.9 + 6 - 1
f(3) = 18 + 5
f(3) = 23
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
f(x) = 2x² + 2x - 1
f(-2) = 2.(-2)² + 2.(-2) - 1
f(-2) = 2.4 - 4 - 1
f(-2) = 8 - 5
f(-2) = 3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
f(x) = 2x² + 2x - 1
f(0) = 2.0² + 2.0 - 1
f(0) = - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
f)
f(x) = 2x² + 2x - 1
f(1) = 2.1² + 2.1 - 1
f(1) = 2.1 + 2 - 1
f(1) = 2 + 2 - 1
f(1) = 4 - 1
f(1) = 3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
f(1/3) = 2.(1/3)² + 2.1/3 - 1
f ( 1) = 2 . 1² + 2. 1 - 1
----- ------ -----
( 3) 3² 3
f(1/3) = 2. 1 + 2 - 1
----- -----
9 3
f(1/3) = 2 + 2 - 1
------ -----
9 3
2 + 6 - 9 8 - 9 - 1
f(1/3) = --------------- = ----------- = ------
9 9 9
**************************************
2.
f(x) = x² - 3x + 2
f(2) = 2² - 3.2 + 2
f(2) = 4 - 6 + 2
f(2) = 4 + 2 - 6
f(2) = 6 - 6
f(2) = 0
f(x) = x² - 3x + 2
f(-3) = (-3)² - 3.(-3) + 2
f(-3) = 9 + 9 + 2
f(-3) = 18 + 2
f(-3) = 20
f(x) = x² - 3x + 2
f(0) = 0² - 3.0 + 2
f(0) = 2
f(2) + f(-3) = 0 + 20
----------------- ----------- = 20/2 = 10
f(0) 2
*****************************************
3.
a)
f(x) = x² - 4x + 3
0 = x² - 4x + 3
x² - 4x + 3 = 0
a = 1; b = - 4; c = 3
Δ = b² - 4ac
Δ = (-4)² - 4.1.3
Δ = 16 - 12
Δ = 4
x = - b +/- √Δ = - ( - 4) +/- √4
-------------- ---------------------
2a 2.1
x = 4 + 2
--------- = 6/2 = 3
2
x = 4 - 2 = 2/2 = 1
--------
2
***********************************
b)
f(x) = 2x² - 2x - 4
0 = 2x² - 2x - 4
2x² - 2x - 4 = 0 (:2)
x² - x - 2 = 0
a = 1; b = - 1; c = - 2
Δ = b² - 4ac
Δ = (-1)² - 4.1.(-2)
Δ = 1 + 8
Δ = 9
x = - b +/- √Δ = - (-1) +/- √9
--------------- ------------------
2a 2.1
x = 1 + 3
---------- = 4/2 = 2
2
x = 1 - 3 = - 2/2 = - 1
---------
2
*****************************************
c)
f(x) = x² - 9
0 = x² - 9
9 = x²
x² = 9
x = √9
x = 3 e x = - 3
*****************************************
d)
f(x) = x² + 3x + 2
0 = x² + 3x + 2
x² + 3x + 2 = 0
a = 1; b = 3; c = 2
Δ = b² - 4ac
Δ = 3² - 4.1.2
Δ = 9 - 8
Δ = 1
x = - b +/- √Δ = - 3 +/- √1
------------- -------------------
2a 2.1
x = - 3 + 1
---------- = - 2/2 = - 1
2
x = - 3 - 1 = -4/2 = - 2
----------
2
****************************************
e)
f(x) = x² - 4x + 4
0 = x² - 4x + 4
x² - 4x + 4 = 0
a = 1; b = - 4; c = 4
Δ = b² - 4ac
Δ = (-4)² - 4.1.4
Δ = 16 - 16
Δ = 0 (uma raiz)
x = - b +/- √Δ = - (-4) +/- √0
---------------- -----------------
2a 2.1
x = 4/2
x = 2
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