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Math Help - Equation of Parabola

  1. #1
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    Equation of Parabola

    What is the equation of a parabola that goes through points (0,1), (–1,6),and (2,3)?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    What is the equation of a parabola that goes through points (0,1), (–1,6),and (2,3)?
    Substitute the given points into the model y = ax^2 + bx + c:

    (0, \, 1) \Rightarrow 1 = c.

    Update the model:

    y = ax^2 + bx + 1.

    (-1, \, 6) \Rightarrow 6 = a - b + 1 \Rightarrow a - b = 5 .... (1)

    (2, \, 3) \Rightarrow 3 = 4a + 2b + 1 \Rightarrow 2a + b = 1 .... (2)

    Solve equations (1) and (2) simultaneously.
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  3. #3
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    great

    Quote Originally Posted by mr fantastic View Post
    Substitute the given points into the model y = ax^2 + bx + c:

    (0, \, 1) \Rightarrow 1 = c.

    Update the model:

    y = ax^2 + bx + 1.

    (-1, \, 6) \Rightarrow 6 = a - b + 1 \Rightarrow a - b = 5 .... (1)

    (2, \, 3) \Rightarrow 3 = 4a + 2b + 1 \Rightarrow 2a + b = 1 .... (2)

    Solve equations (1) and (2) simultaneously.
    I thank you very much.
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