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How do i find the equation of a parabola in the form ax^2+bx+c?

  • Math -

    If y = f(x) = a x^2 + b x + c
    and a, b and c are constants
    then you have your parabola.
    That IS one.
    Now do you want some particular parabola?
    for example if I want a parabola that opens up (holds water) and has a vertex at x = 4 and y = -5
    Then I can use the form:
    (x-h)^2 = 4 g (y-k)
    where (h,k) is the vertex and it will open up if g is positive. (by the way g is the distance from the vertex to the focus)
    The constant g determines how "steep" it is.
    so for our vertex at (4, -5) I have
    (x-4)^2 = 4 g (y+5)
    for our example let's take g = 1/4 to make it simple
    x^2 -8 x +16 = y + 5
    y = x^2 -8 x + 11
    which is your form that you wanted

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