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Math Help - Writing Parabola Equations

  1. #1
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    Writing Parabola Equations

    Please help me with this, the teachers are on spring break for another week and i would really like to figure this out. I'm thinking that there is supposed to be two x-intercepts, not an x and y.

    Here is the question:

    Write the equation for the parabola in the form  y=a(x-h)^2+k with a y-intercept 10, x-intercept 2, and equation of axis of symmetry x-3=0
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  2. #2
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    Quote Originally Posted by nuckers View Post
    Please help me with this, the teachers are on spring break for another week and i would really like to figure this out. I'm thinking that there is supposed to be two x-intercepts, not an x and y.

    Here is the question:

    Write the equation for the parabola in the form  y=a(x-h)^2+k with a y-intercept 10, x-intercept 2, and equation of axis of symmetry x-3=0
    x = h is the axis of symmetry ...

    y = a(x-3)^2 + k

    10 = a(0-3)^2 + k ... y-intercept

    0 = a(2-3)^2 + k ... x-intercept

    solve for a and k
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  3. #3
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    Quote Originally Posted by skeeter View Post
    x = h is the axis of symmetry ...

    y = a(x-3)^2 + k

    10 = a(0-3)^2 + k ... y-intercept

    0 = a(2-3)^2 + k ... x-intercept

    solve for a and k
    Thanks, but thats what i did, but when i input it into my graphing calculator i don't get the x-intercept of 2, it comes out as 2.55

    I ended up with the equation y=10/9(x-3)^2
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  4. #4
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    Quote Originally Posted by nuckers View Post
    Thanks, but thats what i did, but when i input it into my graphing calculator i don't get the x-intercept of 2, it comes out as 2.55

    I ended up with the equation y=10/9(x-3)^2
    10 = 9a+k

    0 = a+k

    try again.
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  5. #5
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    Ha Ha
    K, i think i got it, just did a few things backwards
    y=100/81(x-3)^2-10/9

    Thanks so much for your help
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  6. #6
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    Quote Originally Posted by nuckers View Post
    Ha Ha
    K, i think i got it, just did a few things backwards
    y=100/81(x-3)^2-10/9

    Thanks so much for your help
    ... sorry, but that is not correct.


    10 = 9a + k

    0 = a+k ... k = -a

    10 = 9a + (-a)

    10 = 8a

    a = \frac{10}{8} = \frac{5}{4}

    k = -a = -\frac{5}{4}


    y = \frac{5}{4}(x - 3)^2 - \frac{5}{4}
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  7. #7
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    wow, i wasn't even close, not i have to figure out what i was doing wrong

    Thank you for your help
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