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Math Help - Determining the values of a, b and c for quadratic function given some limits.

  1. #1
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    Determining the values of a, b and c for quadratic function given some limits.

    Hey, having some problems with this problem. I honestly have no idea how to go about solving it, which is why I came here.

    Question:

    Determine the real values of a, b, and c for the quadratic function f(x) = ax^2 + bx + c, a cannot equal 0, that satisfy the conditions: f(0) = 0, 'limit as x approaches 1' = 5, and 'limit as x approaches -2' = 8.

    I know that these points are in the function, the y intercept is 0 (don't know how that helps), and it looks like there are no discontinuities in this function.

    Any help is greatly appreciated!

    - Steve
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  2. #2
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    Quote Originally Posted by Kakariki View Post
    Hey, having some problems with this problem. I honestly have no idea how to go about solving it, which is why I came here.

    Question:

    Determine the real values of a, b, and c for the quadratic function f(x) = ax^2 + bx + c, a cannot equal 0, that satisfy the conditions: f(0) = 0, 'limit as x approaches 1' = 5, and 'limit as x approaches -2' = 8.

    I know that these points are in the function, the y intercept is 0 (don't know how that helps), and it looks like there are no discontinuities in this function.

    Any help is greatly appreciated!

    - Steve
    Since quadratic functions are continous we know that

    \lim_{x \to a}f(x)=f(a), \forall x \in\mathbb{R}

    Using this fact we get

    0=a0^2+b0+c \iff c=0
    5=a(1)^2+b(1)+c
    8=a(-2)^2+b(-2)+c

    Solving this system of equations gives a=3, b=2, c=0

    So the desired quadratic is

    f(x)=3x^2+2x
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    Since quadratic functions are continous we know that

    \lim_{x \to a}f(x)=f(a), \forall x \in\mathbb{R}

    Using this fact we get

    0=a0^2+b0+c \iff c=0
    5=a(1)^2+b(1)+c
    8=a(-2)^2+b(-2)+c

    Solving this system of equations gives a=3, b=2, c=0

    So the desired quadratic is

    f(x)=3x^2+2x
    That makes sense, but how do you go about solving the 'system of equations'?
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    [snip]
    0=a0^2+b0+c \iff c=0

    5=a(1)^2+b(1)+c

    8=a(-2)^2+b(-2)+c

    [snip]
    Quote Originally Posted by Kakariki View Post
    That makes sense, but how do you go about solving the 'system of equations'?
    The first one is simple.

    Substitute the value of c into the second and third equations and simplify them. Now solve those two equations simultaneously
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