1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding the function of a Parabola