kryton1212
The graph of y=ax^(2)+bx+c is given as shown. Which of the following is / are true?
I. a<0
II. b<0
III. c<0
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
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kryton1212
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|dw:1352549825053:dw|
Kira_Yamato
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(C)
c < 0 as graph cuts y-axis below the x-axis
a < 0 because graph is frowning curve
hashsam1
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E)
inverted U shape meaning a<0
intersecting y axis at negative means C is less than 0 c<0
and also there is shift along x axis in right direction means b<0
Kira_Yamato
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Overlooked the detail for b<0... Sorry
kryton1212
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I am confusing why b>0 is correct
sirm3d
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the line of symmetry x = -b/2a, is a positive value, and we know a < 0 so b > 0
kryton1212
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I am sorry that I type it wrongly.
It should be : "I am confusing why b<0 is correct"
sirm3d
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b > 0 is correct.
kryton1212
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why
03225186213
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a<0 because parabola opens downward
kryton1212
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I know a<0 and c<0, I just don't know why b<0 is correct
sirm3d
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b < 0 is NOT correct.
kryton1212
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so the answer is C?
sirm3d
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yes. a < 0 and c < 0.
hashsam1
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|dw:1352551798883:dw|
sirm3d
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@hashsam1 the line of symmetry is the line x = -b/2a. according to the graph it is to the right of the y-axis (so the sign of -b/2a is positive). we know that a < 0, so if b < 0 then the sign of -b/2a is -(-)/2(-) is negative.
phi
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a simple example with 2 positive roots x=1 and x=2
the polynomial would be -(x-1)(x-2) = -x^2 +3x -2
this suggests a<0 b>0 c<0
kryton1212
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I understand now, thank you so much :)
kryton1212
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another question
If f(x)=x-(1/x), then f(x)-f(1/x)= ?
hashsam1
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oops yes right i over looked the equation thinking its just a normal quadratic equation.
phi
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If f(x)=x-(1/x), then f(x)-f(1/x)= ?
replace f(x) with x- 1/x
replace f(1/x) with 1/x - x
kryton1212
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|dw:1352552240065:dw|
sirm3d
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yes
kryton1212
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|dw:1352552332194:dw|
sirm3d
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yup, that's right.
kryton1212
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|dw:1352552484497:dw|
sirm3d
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1/(1/x) = x. try again.
kryton1212
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oh -.-|dw:1352552602486:dw|
sirm3d
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you still need to combine x + x
kryton1212
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2x-(2/x)
sirm3d
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that's right!
kryton1212
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|dw:1352552793347:dw|
sirm3d
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i'll accept either form.
kryton1212
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another question
If f(x)=10^(2x), then f(4y)=?
kryton1212
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A. 10^(4y).
B. 10^(2+4y)
C. 10^(8y)
D. 40^(y)
E. 40^(2y)
sirm3d
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replace x by 4y, what do you get?
kryton1212
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B ?
sirm3d
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C it is.
kryton1212
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oh yes
sirm3d
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\[\huge 10^{2(4y)}\]
nubeer
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f(x)=10^(2x)
f(x)=10^(2(4y))
kryton1212
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If f(x)=x/(1-x), then f(1/x)f(-x)=?
kryton1212
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@gerryliyana
sirm3d
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and your answer is?
kryton1212
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|dw:1352553510302:dw|
sirm3d
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\[\huge f(-x) = \frac{ (-x) }{ 1-(-x) }\]
kryton1212
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errrr.....wait
gerryliyana
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If f(x)=x/(1-x), then f(1/x)f(-x)=
f(1/x) = (1/x)/(1-(1/x)) = 1/x((x-1)/x)
f(-x) =(-x)/(1-(-x)) = -x/(1+x)
f(1/x)f(-x) = 1/x((x-1)/x) times -x/(1+x)
f(1/x)f(-x) = -x/(x((x-1)/x)(1+x))
kryton1212
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o.o errrr.... wait a moment
gerryliyana
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f(1/x)f(-x) = -x/(x((x-1)/x)(1+x))
f(1/x)f(-x) = -x/((x-1)(x+1))
kryton1212
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|dw:1352554094668:dw|
kryton1212
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sirm3d
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|dw:1352554209982:dw|
gerryliyana
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|dw:1352554144569:dw|
kryton1212
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is it necessary for you to give me a big cross.......
I got it :)
kryton1212
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gerryliyana
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kryton1212
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sirm3d
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kryton1212
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gerryliyana
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sirm3d
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|dw:1352554649051:dw|
gerryliyana
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sirm3d
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we're not discussing' we're exchanging notes. hahaha
kryton1212
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|dw:1352554679681:dw|
kryton1212
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haha :))
gerryliyana
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kryton1212
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sirm3d
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what's the answer to your problem \[\huge f(\frac{ 1 }{ x })f(-x)\]
kryton1212
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oh my god
kryton1212
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A. -1/2
B. -1
C. -(1-x)/(1+x)
D. x/(1-x^(2))
E. x/(x^(2)-1)
no answer since this is past paper, my teacher haven't give us the answers yet
kryton1212
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I still cannot get the answer
Callisto
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Please start a new post for a new question. If possible, please also put them in the right categories (subtopics). Thanks!
sirm3d
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\[\large f(1/x)f(-x) = \frac{ 1/x }{ 1-1/x }\frac{ (-x) }{ 1-(-x) }\] \[\large = \frac{ -1 }{ 1+x -\frac{ 1 }{ x }-1 } \times \frac{ -x }{ -x }\]
kryton1212
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so complicated....
sirm3d
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just carry out the multiplication and you'll get (D)
kryton1212
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|dw:1352556469608:dw|
I get this only...
gerryliyana
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f(1/x)f(-x) = -x/(x((x-1)/x)(1+x))
f(1/x)f(-x) = -x/((x-1)(x+1))
f(1/x)f(-x) = -x/(x^2 -1)
f(1/x)f(-x) = -x/-(-x^2 +1)
f(1/x)f(-x) = x/(1-x^2)
the answer is D x/(1-x^2)
gerryliyana
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you got it @kryton1212 ???? take it a simply way..,hehe
kryton1212
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confusing................. I think it later
another question
If a,b and c are all positive, which of the following may represent the graph of ax+by+c=0?|dw:1352556954406:dw|
kryton1212
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@hartnn would you kindly help me?
Callisto
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@kryton1212 Please start a new post for a new question!
kryton1212
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the problem is I cannot draw picture in a new post
hartnn
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ok, let this be last question discussed in this post, agreed @kryton1212 ?
for this
u know how to find intercepts ?
Callisto
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You can post the question a draw it in the comment
kryton1212
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@hartnn that's ok. c=y-intecept
hartnn
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nopes, c is y intercept in y=mx+c
not here
hartnn
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to get x intercept, put y=0 in ax+by+c=0
to get y intercept, put x=0 in ax+by+c=0
hartnn
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now tell me what intercepts u get
kryton1212
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....oh yes.
I don't know how to find the intercept in these gaphs
hartnn
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to get x intercept, put y=0
to get y intercept, put x=0
in any graphs
kryton1212
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ax+by+c=0
put y=0???
ax+c=0?
hartnn
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yes, thats right
ax+c=0
x= ?
kryton1212
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x=-c/a?
hartnn
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absolutely correct!
now -c/a is positive or negative ?
hartnn
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given a and c are positive....
kryton1212
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-ve
hartnn
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so your x-intercept is negative, that is it will cut x axis in negative (left) side
got this ?
what about y-intercept ???
kryton1212
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so it may be B or E.
y=-c/b
is it E?
hartnn
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yes, y intercept is also negative, so it will cut down.
and yes its E
clear as to how ?
kryton1212
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clear now, thank you
hartnn
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make sure u ask next question in new post...
phi
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@kryton1212 it would be better if you made each question a separate post.
kryton1212
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okok