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    i thought i done this correctly but according to the mark scheme, i did not...

    the question asks: express 5x^2 + 20x - 8 in the form p(x+q)^2 + r.
    i got 5(x+4)^2 - 95
    but the mark scheme says, 5(x+2)^2 - 28

    i dont understand this!
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    Lets see..
    

5x^2 + 20x - 8

= 5[x^2 + 4x - \frac{8}{5}]
    complete the square from there.
    this may help:
    ax^2 + bx + c



= a[(x + \dfrac{b}{2a})^2 - (\dfrac{b}{2a})^2 + \dfrac{c}{a}]
    it may look complex, but its quite simple. just put the values in and it should work out. The answer given is correct.
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    Its been a while since I had to do this but....

    You have your 5x^2+20x-8

    So it has to be (x+p) - 20 divided by 5 is 4, then to complete the square you need to divide this number by 2 to put it in the brackets.

    (x+2)^2 - then if you multiply this out the c value you get is 4. Multiply this by the 5 which sits outside the brackets and you get 20. You need -8 so the difference is -28 for the c value.

    This then gives the y=5(x+2)^2 -28

    Hope this explains it clearly.
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    5x^2 + 20x - 8 in the form p(x+q)^2 + r.

    So,

    (5x + 10)^2 - 20 - 8

    = (5x + 10)^2 - 28

    = 5(x + 2)^2 - 28

    p = 5
    q = 2
    r = 28
 
 
 
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