quad.py

import fractions

def quadratic(a, b, c):
    s1 = ( (b**2) - (4*a*c) ) ** 0.5
    s2 = 2*a

    ret = [(-b - s1) / s2, (-b + s1) / s2]
    return ret

def curveFromVP(vertex, point):
    """Finds a quadratic curve given vertex and point coordinate pairs.
Returns in the format ("equation string", a), where the equation is in
the form y=a(x-h)**2 + k."""
    vX, vY = vertex
    pX, pY = point
    aMult = (pX - vX) ** 2
    ret = fractions.Fraction(pY - vY, aMult)

    if ret == 1: retA = ""
    elif ret._denominator == 1: retA = str(ret)
    else: retA = "({})".format(ret)

    if vX == 0:
        retX = "x"
    else:
        retX = "(x{0:+})".format(-vX)

    if vY == 0:
        retY = ""
    elif vY < 0:
        retY = " - {}".format(abs(vY))
    else:
        retY = " + {}".format(abs(vY))

    retStr = "f(x) = {}{}**2{}".format(retA, retX, retY)

    return retStr, ret