AS Maths Question help- minimum point and Geometrical transformation

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    Please can someone help with this question, kind of understand it but don't feel confident..

    A) x^2 - 7x + 2 in the form (x-p)^2

    I did (x - 7/2)^2 - 41/4


    B) Hence write down the minimum value of x^2 - 7x + 2
    Is this just -41/4? I'm not sure

    C) Describe the geometrical transformation which maps the graph of x^2 - 7x + 2 onto y= (x-4)^2

    I really don't understand this one, please help! Thank you
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    (Original post by jazz_xox_)
    Please can someone help with this question, kind of understand it but don't feel confident..

    A) x^2 - 7x + 2 in the form (x-p)^2

    I did (x - 7/2)^2 - 41/4

    B) Hence write down the minimum value of x^2 - 7x + 2
    Is this just -41/4? I'm not sure
    Perfect. I assume the question was to write it in the form (x-p)^2 + q though.


    C) Describe the geometrical transformation which maps the graph of x^2 - 7x + 2 onto y= (x-4)^2

    I really don't understand this one, please help! Thank you
    You have f(x) = (x-7/2)^2 - 41/4. Then f(x + a) + b = (x+a - 7/2)^2 - 41/4 + b. So what a,b do you need to turn f(x) into (x-4)^2?
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    (Original post by Zacken)
    Perfect. I assume the question was to write it in the form (x-p)^2 + q though.
    You have f(x) = (x-7/2)^2 - 41/4. Then f(x + a) + b = (x+a - 7/2)^2 - 41/4 + b. So what a,b do you need to turn f(x) into (x-4)^2?
    Yes that was the part A of the question I get that it needs to be a translation (I think?) but still don't understand the formatting of it. This has never been my strong point
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    (Original post by jazz_xox_)
    Yes that was the part A of the question I get that it needs to be a translation (I think?) but still don't understand the formatting of it. This has never been my strong point
    So, you need to do a horizontal translation to turn the x-7/2 into a x-4 that's f(x+a) and a vertical transalation to turn the -41/4 to a -0 (that's f(x) + b)

    Like I referred to in my previous post, what values for a and b do you need to choose for that to happen?
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    (Original post by Zacken)
    So, you need to do a horizontal translation to turn the x-7/2 into a x-4 that's f(x+a) and a vertical transalation to turn the -41/4 to a -0 (that's f(x) + b)

    Like I referred to in my previous post, what values for a and b do you need to choose for that to happen?
    Is it A= 1/2 and B +41/4?? Sorry if I'm completely off and thanks for your help!!
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    (Original post by jazz_xox_)
    Is it A= 1/2 and B +41/4?? Sorry if I'm completely off and thanks for your help!!
    Perfect! So that corresponds to a horizontal translation to the [what direction? Right or left?] by [how many?] units and a vertical translation in [what direction? up or down?] by [how many?] units.

    Reminder: f(x+a) is a horizontal transaltion to the left by a units and f(x) + b is a vertical translation upwards by b units.
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    (Original post by Zacken)
    Perfect! So that corresponds to a horizontal translation to the [what direction? Right or left?] by [how many?] units and a vertical translation in [what direction? up or down?] by [how many?] units.

    Reminder: f(x+a) is a horizontal transaltion to the left by a units and f(x) + b is a vertical translation upwards by b units.
    Yay thank you soo much! A horizontal translation to the right by 1/2 units and a vertical translation up by 41/4 units? Thanks again, you are a life saver
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    (Original post by jazz_xox_)
    Yay thank you soo much! A horizontal translation to the right by 1/2 units and a vertical translation up by 41/4 units? Thanks again, you are a life saver
    Perfect.
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    (Original post by Zacken)
    Perfect.
    Yay! I've just seen on your page that you are studying at Cambridge, wow -congratulations! Wishing you the best of luck
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    (Original post by jazz_xox_)
    Yay! I've just seen on your page that you are studying at Cambridge, wow -congratulations! Wishing you the best of luck
    Thank you very much.
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    (Original post by Zacken)
    Thank you very much.
    You're going to be told something similar about once a week for the rest of your life.
 
 
 
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