Equation for parabola

  1. Vertex (-5,5) point (-3,17)

    Equation for the parabola with the given vertex that passes through the given point.

    I am stumped! Please help :bugeye:
     
  2. jcsd
  3. well, look at this
    you have a quadratic of the form ax^2+bx+c
    so you have two points
    so plug in y and x in for those two points:

    5=25a-5b+c
    and
    17=9a-3b+c

    but they also tell you that (-5, 5) is the vertex
    which means that there, the solution only has one root; meaning that the x coordinate is equal to -b/2a
    so then you have
    -5=-b/2a

    i think you should be able to solve for this now. perhapsably.
     
  4. Using what is provided, I have come up with:

    y=3(x+5)^2+5
     
  5. Galileo

    Galileo 1,999
    Science Advisor
    Homework Helper

    Great. This is always the most insightful way to write the equation of a parabola.
    As a check, you can easily see the vertex is at (-5,5). Putting x=-3 gives y=3(2^2)+5=17.
     
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