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Math Help - Equation of a porabola

  1. #1
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    Equation of a porabola

    Hi I was hoping someone could help me with a math problem I am confused about. If you could, please use simple steps. Thank you

    Here is what the problem looks like:

    The graph of a parabola passes through the three points (0,3), (1,2), (2,3). Find the values of a, b, c and write the equation of the parabola in the form y = ax^2 + bx +c.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Troy S View Post
    Hi I was hoping someone could help me with a math problem I am confused about. If you could, please use simple steps. Thank you

    Here is what the problem looks like:

    The graph of a parabola passes through the three points (0,3), (1,2), (2,3). Find the values of a, b, c and write the equation of the parabola in the form y = ax^2 + bx +c.
    This is a simultaneous equations problem. You will get three equations and three unknowns. Here's how:

    For (0,3) => x = 0, y = 3
    so y = ax^2 + bx + c becomes
    3 = a(0)^2 + b(0) + c
    => c = 3
    ah, so we found c from the first, yah! This means we will only need to solve 2 equations. This will turn out easier than i thought.

    For (1,2) => x = 1, y = 2
    so y = ax^2 + bx + c becomes
    2 = a(1)^2 + b(1) + c .........remember, c=3
    => 2 = a + b + 3
    => a + b = -1 ...........(1)

    For (2,3) => x = 2, y = 3
    so y = ax^2 + bx + c becomes
    3 = a(2)^2 + b(2) + c .........remember, c = 3
    => 3 = 4a + 2b + 3
    => 4a + 2b = 0 ..............(2)

    So we found c, to find a and b we need to solve the system:
    a + b = -1 ................(1)
    4a + 2b = 0 ..............(2)

    => 2a + b = 0 ...............(2)/2
    ......a + b = -1 ..............(1)
    => a = 1

    but a + b = -1
    => 1 + b = -1
    => b = -2

    so our parabola is:
    y = x^2 - 2x + 3
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  3. #3
    Bar0n janvdl's Avatar
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    y = a(x - p)^2 + q
    = a(x - 1)^2 + 2 [Take the turning point of the parabola and insert it into the p and q values]

    = a(x^2 - 2x + 1) + 2

    Set (2;3) in the equation. x = 2 ; y = 3

    3 = a((2^2) - (2 x 2) + 1) + 2
    3 = a(1) + 2
    3 = a + 2
    a = 1

    Thus y = x^2 - 2x + 3


    Hope this helps.
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  4. #4
    Bar0n janvdl's Avatar
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    If i might give you a tip, physically draw the parabola when you are given info like this. It really helps you to understand it and you will see the bigger picture
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  5. #5
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    Thank you, both of you.
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