algebra

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A parabola has x-intercepts at 3 and 7, a y-intercept at -21, and (5,4) for its vertex. Write the parabola’s equation

  • algebra -

    Sketch those points on a graph.
    It is an upside down parabola (sheds water)
    The axis of symmetry is x = 5
    when x = 5, y = 4
    so
    for starters
    y-4 = c (x-5)^2
    That is the same both sides of x = 5
    and y = 4 when x = 5
    We need c
    put in one of those other points
    for example (0,-21)
    -21 -4 = c (-5)^2
    -25 = c (25)
    c = -1
    so
    y-4 = -(x-5)^2
    or
    y = 4 - (x-5)^2

    check with (3,0)
    ? = 4 -(-2)^2
    ? = 4 - 4
    0 sure enough

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