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    f(x)=(x-1)(x+2) So its a parabola which crosses the x axis at 1 and -2 obviously.

    for part one you shift it 2 to the left so now the x intercepts become -4 and -1.

    If you don't see how to draw f(x) expand it it may help.
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    (Original post by whydoidothis?)
    The textbook is right.
    I have a feeling it is. can you explain? please
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    (Original post by samantham999)
    I have a feeling it is. can you explain? please
    I explained it ealier on in the thread, just incase you missed it.
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    (Original post by whydoidothis?)
    f(x)=(x-1)(x+2) So its a parabola which crosses the x axis at 1 and -2 obviously.

    for part one you shift it 2 to the left so now the x intercepts become -4 and -1.

    If you don't see how to draw f(x) expand it it may help.

    I LOVE YOU.
    i understand, thank you so much
    I knew you had to do something with the equation they gave
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    (Original post by samantham999)
    I LOVE YOU.
    i understand, thank you so much
    I knew you had to do something with the equation they gave
    no problem, just get used to reading these types of questions. You knew how to do it, i could tell. If you need any help with AS maths you can PM me. I finished A level maths and got 98% at AS.
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    (Original post by samantham999)
    I thought I was supposed to shift this 2 spaces to the left?
    Question 2Bi
    for 2a did you draw something that looked a little like this;

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    (Original post by DylanJ42)
    for 2a did you draw something that looked a little like this;

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    Yes thats correct, you just make x-1=0 and x+2=0
    you get 1 & -2

    the y intercept is -1x2 (-2)
    and then plot
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    (Original post by whydoidothis?)
    no problem, just get used to reading these types of questions. You knew how to do it, i could tell. If you need any help with AS maths you can PM me. I finished A level maths and got 98% at AS.
    Wow, thats impressive! well done
    I'm doing 6 units this year, I'm finishing chapter 4 in c1 and i'm finding it okayish
    I'm really determined to get an A*

    Are you studying maths at uni?
    and i will pm you for sure when i'm stuck, thanks so much
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    (Original post by samantham999)
    Yes thats correct, you just make x-1=0 and x+2=0
    you get 1 & -2

    the y intercept is -1x2 (-2)
    and then plot
    ah someones already helped you, I was just going to say how from this graph is easy to see how shifting everything to the left bt two will give you the graph shown in the answer book
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    (Original post by DylanJ42)
    ah someones already helped you, I was just going to say how from this graph is easy to see how shifting everything to the left bt two will give you the graph shown in the answer book
    thanks anyway
    for 2bii) f(x) + 2
    I shift 2 unit up right?

    and do I start originally from the f(x) = (x-1) (x+2) sketch?
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    I took C1-4 FP1-2 if you need any help just pm

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    (Original post by samantham999)
    I will. I know how to do fx notation with exam solutions but this answer in the textbook doesn't even make sense

    did you get an A/A* in maths a level?
    i'm doing 6 units this year!! tips?
    I took C1-4 and FP1-2

    If you need any help just pm

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    (Original post by maruchan)
    I took C1-4 FP1-2 if you need any help just pm

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    thank you! i will x
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    (Original post by samantham999)
    thanks anyway
    for 2bii) f(x) + 2
    I shift 2 unit up right?

    and do I start originally from the f(x) = (x-1) (x+2) sketch?
    yea thats exactly what you do

    and you do start with (x-1)(x+2) yea

    basically when you were doing f(x+2) what you are actually doing when you "shift the graph two units to the left" is replacing all the "x"s you see in the function with "x + 2"s.

    Think of it like this, if f(x) = (x-1)(x+2)
    then you could also say, f(q) = (q-1)(q+2)
    or if you really wanted, f() = (-1)(+2) where just like x and q, the just represents a number

    so if you have f(x+2) you get ((x+2)-1)((x+2)+2) = (x+1)(x+4). This is what you drew in part 2b)i).

    Then with f(x) + a, you just write down your function, in this case f(x) is (x-1)(x+2) and stick + a on the end

    So, f(x) + a = (x-1)(x+2) + a

    And in your case f(x) + 2 = (x-1)(x+2) + 2, which results in the shift upwards of 2 units when you draw the graph
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    (Original post by DylanJ42)
    yea thats exactly what you do

    and you do start with (x-1)(x+2) yea

    basically when you were doing f(x+2) what you are actually doing when you "shift the graph two units to the left" is replacing all the "x"s you see in the function with "x + 2"s.

    Think of it like this, if f(x) = (x-1)(x+2)
    then you could also say, f(q) = (q-1)(q+2)
    or if you really wanted, f() = (-1)(+2) where just like x and q, the just represents a number

    so if you have f(x+2) you get ((x+2)-1)((x+2)+2) = (x+1)(x+4). This is what you drew in part 2b)i).

    Then with f(x) + a, you just write down your function, in this case f(x) is (x-1)(x+2) and stick + a on the end

    So, f(x) + a = (x-1)(x+2) + a

    And in your case f(x) + 2 = (x-1)(x+2) + 2, which results in the shift upwards of 2 units when you draw the graph

    I understand now.
    but is this the answer?
    shouldn't i be back at 0 not going thru it?
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    (Original post by samantham999)
    I understand now.
    but is this the answer?
    shouldn't i be back at 0 not going thru it?
     \displaystyle f(x) = (x-1)(x+2)
     \displaystyle f(x) + 2 = (x-1)(x+2) + 2
     \displaystyle f(x) + 2 = x^2 + x - 2 + 2
     \displaystyle f(x) + 2 = x^2 + x = x(x+1)

    therefore f(x) + 2 crosses the x axis at x=0 and x=-1 as the answer scheme shows
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    (Original post by DylanJ42)
     \displaystyle f(x) = (x-1)(x+2)
     \displaystyle f(x) + 2 = (x-1)(x+2) + 2
     \displaystyle f(x) + 2 = x^2 + x - 2 + 2
     \displaystyle f(x) + 2 = x^2 + x = x(x+1)

    therefore f(x) + 2 crosses the x axis at x=0 and x=-1 as the answer scheme shows
    Ah i feel so dumb, I get the first two but when you expand the bracket how comes you dont do it properly?
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    (Original post by samantham999)
    Ah i feel so dumb, I get the first two but when you expand the bracket how comes you dont do it properly?
    dont do it properly. how do you mean? did you learn to expand brackets with FOIL?
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    (Original post by DylanJ42)
    dont do it properly. how do you mean? did you learn to expand brackets with FOIL?
    i got this by foil
    x2 + 2x - x -2 +2

    x2 + x -2 +2 ?

    how do i get to adding x(x+1) on the end?
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    (Original post by samantham999)
    i got this by foil
    x2 + 2x - x -2 +2

    x2 + x -2 +2 ?
    oh sorry, maybe I should have done it like this;

     \displaystyle f(x) + 2 = (x-1)(x+2) + 2
     \displaystyle f(x) + 2 = (x^2 + 2x - x - 2) + 2

    Now I just simplify the x terms ie simplfy  \displaystyle 2x - x , and im left with;

     \displaystyle f(x) + 2 = (x^2 + x - 2) + 2

    Is that easier to see now?

    Now from here you have  \displaystyle f(x) + 2 = (x^2 + x - 2) + 2

    do you see how the -2 and + 2 "cancel out" leaving you with;

     \displaystyle f(x) + 2 = x^2 + x

    now factoring out an x gives us  \displaystyle f(x) + 2 = x(x + 1)
 
 
 
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