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Thread: Finding the equation of the parabola

  1. #1
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    Finding the equation of the parabola

    Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?
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  2. #2
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    Re: Finding the equation of the parabola

    The equation for a parabola would be knowing the values of $\displaystyle a, b, c$ in $\displaystyle y = ax^2 + bx + c$.

    What does C = (-2,7) on the parabola tell you? It says that when x = -2, the y value of that formula will be 7.

    Thus $\displaystyle (7) = a(-2)^2 + b(-2) + c = 4a - 2b + c$.

    So C on the parabola tells you that $\displaystyle 4a - 2b + c = 7$.

    A and B on the parabola will likewise tell you something. And if you know what a, b, and c are, then you have "found the parabola".
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Finding the equation of the parabola

    Let:

    $\displaystyle y(x)=ax^2+bx+c$

    From the given points, this gives the 3X3 linear system:

    $\displaystyle a(0)^2+b(0)+c=1$

    $\displaystyle a(-1)^2+b(-1)+c=-2$

    $\displaystyle a(-2)^2+b(-2)+c=7$

    Simplified:

    $\displaystyle c=1$ this allows us to reduce the problem to the following 2X2 system

    $\displaystyle a-b=-3$

    $\displaystyle 4a-2b=6$

    Solve this system, and you will have the values of the coefficients $\displaystyle a,b,c$ which will give you the parabola you want.
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    Re: Finding the equation of the parabola

    Quote Originally Posted by Chipset3600 View Post
    Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?
    $\displaystyle y=ax^2+bx+c$. Point A tells us that $\displaystyle c=1$
    Point B tells us $\displaystyle a-b+1=-2$
    Point C tells us $\displaystyle 4a-2b+1=7$
    Now solve for $\displaystyle a~\&~b$.
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  5. #5
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    Re: Finding the equation of the parabola

    f(x) = 6x^2+9x+1
    Thank you very much
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