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Math Help - Writing Quadratic equation

  1. #1
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    Writing Quadratic equation

    Write an equation of the quadratic function f whose graph has x-intercepts 3 and 7 and f(5) = 8.

    I tried foiling the two zeros but that doesn't give me 8 when for f(5).

    Like:
    (x -3)(x - 7)
    x - 10x + 21
    (5) - 10(5) + 21 = -4

    ?
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  2. #2
    Moo
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    Hello

    Quote Originally Posted by Power View Post
    Write an equation of the quadratic function f whose graph has x-intercepts 3 and 7 and f(5) = 8.

    I tried foiling the two zeros but that doesn't give me 8 when for f(5).

    Like:
    (x -3)(x - 7)
    x - 10x + 21
    (5) - 10(5) + 21 = -4

    ?
    This was a good trial
    You're just forgetting something : the leading coefficient.

    a(x-3)(x-7) also has x-intercepts at 3 & 7 , where a is a constant (different to 0, if possible ^^)


    Then use f(5)=8 to determine a.
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  3. #3
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    0 = a(x - 3)(x - 7)
    8 = a(5 - 3)(5 - 7)
    -2 = a ??

    I dont think thats right. Please help further.
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  4. #4
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    Quote Originally Posted by Power View Post
    y = a(x - 3)(x - 7)
    8 = a(5 - 3)(5 - 7)
    -2 = a ??

    I dont think thats right. Please help further.
    Why do you think this isn't right ? It's exactly the solution

    Though you can expand -2(x-3)(x-7) in order to get a quadratic form... You can choose whatever display you want^^
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  5. #5
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    Quote Originally Posted by Power View Post
    0 = a(x - 3)(x - 7)
    8 = a(5 - 3)(5 - 7)
    -2 = a ??

    I dont think thats right. Please help further.
    What's the problem?

    f(x) = -2(x - 3)(x - 7)

    f(3) = 0

    f(7) = 0

    f(5) = -2(2)(-2) = 8
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  6. #6
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    I got it, I just made an arithmetic mistake while checking my answer.
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