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Math Help - Quadratic Function

  1. #1
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    Quadratic Function

    f is a quadratic function such that  f(0) = 0, f(1) = 2, and  f(-1) = 2. Find an equation for  f(x)
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  2. #2
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     f(x) = ax^2+bx+c

    or

     f(x) = a(x-b)^2+c

    Choose one form and use your co-ordinates to substitute and then solve.

    Here's a start...

     f(x) = ax^2+bx+c

     f(0) = 0 \Rightarrow 0 = a\times 0^2+b\times 0 +c \Rightarrow c=0

    So we now have  f(x) = ax^2+bx+0

     f(1) = 2 \Rightarrow 2 = a\times 1^2+b\times 1 \Rightarrow 2 = a+b

    Now your turn for

     f(-1) = 2
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  3. #3
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    Okay, well I understand what to do now, but I have some questions. Why for f(1) do you not include c, and I'm assuming for f(-1) you don't include it either. Then after you have solved all of them, do you have to plug them back into the quadratic or can you just leave it as c=0, 2= a+b, etc..
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  4. #4
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    Quote Originally Posted by SHiFT View Post
    Okay, well I understand what to do now, but I have some questions. Why for f(1) do you not include c,
    because we have already found c to be zero


    Quote Originally Posted by SHiFT View Post
    and I'm assuming for f(-1) you don't include it either.
    True for the same reason above.

    Quote Originally Posted by SHiFT View Post
    Then after you have solved all of them, do you have to plug them back into the quadratic or can you just leave it as c=0, 2= a+b, etc..
    Yep after you have a solution for each a,b and c.

    You need to solve for a and b with simultaneous equations first.
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  5. #5
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    so i need to set a-b and a+b in a equation to solve for them?
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  6. #6
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    Talking

    Quote Originally Posted by SHiFT View Post
    so i need to set a-b and a+b in a equation to solve for them?
    I'm not sure what you mean by this...?

    Instead, try using the set-up that the other helper provided to you: Plug the given x-values into the general formula for a quadratic, simplify, and set equal to the given f-values. Solve the resulting system of linear equations by whatever method you prefer of the ones you learned in an earlier algebra course.
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