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Finding equation with zeroes and max value

  1. Feb 21, 2016 #1
    [Note: Thread moved to this forum by a mentor]

    Hi all, the full question is:
    A parabola has zeroes at 5/2 and -3/2 and has an optimal value of 4. Determine equation of the parabola in factored form.

    So I started out with 4 as my y-value on my vertex then took the zeroes(5/2 and -3/2), added them and divided by 2 to get the x-axis for the x-value in the vertex.
    Subbed in (.5,4) into factored form with the zeroes,
    y=a(x-r)(x-s)
    4=a(.5-5/2)(.5-(-3/2)
    4=a(-2)(2)
    4/-4=a
    -1=a
    So the equation should be y=-1(x-5/2)(x-(-3/2) or y=-1(2x-5)(2x+3)
    The answer sheet says its y=-1/4(2x-5)(2x+3)
    I have similar numbers but dont know where I went wrong. Any help is appreciated
     
    Last edited by a moderator: Feb 21, 2016
  2. jcsd
  3. Feb 21, 2016 #2

    fresh_42

    Staff: Mentor

    How did your second equation derive? What does an optimal value of 4 really mean?
     
  4. Feb 21, 2016 #3
    isnt optimal value max value of y which would be the vertex
     
  5. Feb 21, 2016 #4

    SammyS

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    I suppose so, which would follow from 4 being the maximum value. The other common possibility being that it's a minimum, but then of course that would imply that there are no x-intercepts.
     
  6. Feb 21, 2016 #5

    fresh_42

    Staff: Mentor

    It may be a maximum, or a minimum. Anyway, how do you usually find it and where? All you know is the y value of 4 I guess.

    Where does this line come from?
    But maybe you are using another method than me. However, to find your deviation from the given result I need to know better what you are trying to do.

    EDIT: Ok, I got it now. Everything is fine but the way you got rid of the factor 1/2 in the parenthesis. You multiplied twice by two and didn't correct it outside.
     
  7. Feb 21, 2016 #6
    Thanks for the help guys, a buddy of mine solved it and showed me how. I wasnt simplifying x-5/2 into 2x-5 and x--3/2 into 2x+5 before is subbed in my vertex values and thats where I went wrong
     
  8. Feb 21, 2016 #7

    SammyS

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    Those answers are equivalent. except for the part crossed out
     
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