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Math Help - [SOLVED] Line of Symmetry of a Function

  1. #1
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    Cool [SOLVED] Line of Symmetry of a Function

    Q) The function f is defined by f : x → 2x^2 − 12x + 13 for 0 ≤ x ≤ A, where A is a constant

    (i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.

    (ii) State the value of A for which the graph of y = f(x) has a line of symmetry

    (iii) When A has this value, find the range of f

    My Attempt

    2x^2-12x+13

    2(x-3)^2-5

    Now I have no clue on how to do (ii) which is linked with (iii). Will appreciated your help!

    Thanks!
    Last edited by unstopabl3; May 7th 2010 at 11:04 AM.
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  2. #2
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    Quote Originally Posted by unstopabl3 View Post
    Q) The function f is defined by f : x → 2x2 − 12x + 13 for 0 ≤ x ≤ A, where A is a constant

    (i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.

    (ii) State the value of A for which the graph of y = f(x) has a line of symmetry

    (iii) When A has this value, find the range of f

    My Attempt

    2x^2-12x+13

    2(x-3)^2-5

    Now I have no clue on how to do (ii) which is linked with (iii). Will appreciated your help!

    Thanks!
    Obviously, the axis of symmetry should be the line x=3. (You should see this if you plot the graph of this function.)
    Therefore A=6. (If we exclude the degenerate case A=0.)
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  3. #3
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    What values would we take to plot the graph of this manually (with no graphing calculators) function in the quickest possible way on a graph paper during a test or exam? Kindly do elaborate.

    Thanks!
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  4. #4
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    Quote Originally Posted by unstopabl3 View Post
    What values would we take to plot the graph of this manually (with no graphing calculators) function in the quickest possible way on a graph paper during a test or exam? Kindly do elaborate.

    Thanks!
    I guess you can sketch y=x^2 - it goes through (0,0),(1,1),(2,4) (and symmetrically on the left).
    The graph of y=2*x^2 is similar, but all points are in the double height -- it goes through (0,0),(1,2),(2,8).
    Your function is 2(x-3)^2-5 - so you simply have to move the graph of y=2x^2 3 units to the right and 5 units lower.

    (I hope I was able to express myself clearly despite not being native English speaker.)
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  5. #5
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    Also I tried to get the range and I got y= -5 and y= 13. Is this correct?

    Yes, I understood that, but wouldn't that take a lot of time (5-10 mins) for such a question which has 2-4 marks maximum.

    Thanks!
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  6. #6
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    Quote Originally Posted by unstopabl3 View Post
    Also I tried to get the range and I got y= -5 and y= 13. Is this correct?
    Yes, the range is correct.

    Quote Originally Posted by unstopabl3 View Post
    Yes, I understood that, but wouldn't that take a lot of time (5-10 mins) for such a question which has 2-4 marks maximum.

    Thanks!
    I am definitely not in the position to answer this question. However, the amount of time you spend with a question during a test depends on how much practice you have and whether you have done some similar exercises before. So I think it's good that you're working hard and you're learning things in this forum.
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  7. #7
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    Yeah I guess you are right, I will practice graphing these kind of functions a bit more.
    Thanks!

    P.S

    Your English is not bad at all haha
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