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Finding the function of a Parabola

  1. Aug 7, 2009 #1
    1. The graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all number less than or equal to 4. Determine an expression for the function.

    2. none

    3. I do not know how to use the intercepts and the range and manipulate it in to a function. Can you show me step by step? Thank You!
  2. jcsd
  3. Aug 7, 2009 #2
    The parabola has formula y=A(x+B)2+C
    You got the intercepts i.e y=0, x1=-1, x2=3

    Have you ever learned about Vieta's formulas?




    You already got the solutions of the quadratic equation.
  4. Aug 7, 2009 #3


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    Staff: Mentor

    In general, the graph of a parabola is given by the equation y = ax2 + bx + c, which can also be written as y = a(x - r1)(x - r2). Since you are given the two x-intercepts, you should be able to figure out what r1 and r2 are in the second equation I showed.

    So all you need to do is determine that value of a.

    Since the range is all numbers <= 4, the parabola opens downward. The vertex of a parabola is a point on the parabola that is lower than all others (for a parabola that opens upward) or higher than all others (for one that opens downward). The vertex is always midway between the two x-intercepts, provided that there are two x-intercepts. With this information you should be able to find the coordinates of the vertex, and from them the value of a in the parabola's equation.
  5. Aug 15, 2009 #4
    Ok Thank You!
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