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Math Help - Parabola problem - Solving for an unknown 'constant'

  1. #1
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    Parabola problem - Solving for an unknown 'constant'

    The problem that I've been trying to figure out for the last couple hours:

    When the parabola y = x^2 - a(x+1) +3 intersects the x-axis at one point,
    then a= 1. ____ or 2. _____

    Of course you set the y = 0
    then while solving it comes to a point where I have to use the quadratic formula and comes out to:

    a +- sqrt{(a+6)(a-2)}
    2

    After that, I don't know what to do. How do I apply the statement 'intersects the x-axis at one point' to the formula?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by gundanium View Post
    The problem that I've been trying to figure out for the last couple hours:

    When the parabola y = x^2 - a(x+1) +3 intersects the x-axis at one point,
    then a= 1. ____ or 2. _____

    Of course you set the y = 0
    then while solving it comes to a point where I have to use the quadratic formula and comes out to:

    a +- sqrt{(a+6)(a-2)}
    2

    After that, I don't know what to do. How do I apply the statement 'intersects the x-axis at one point' to the formula?
    If a parabola has only 1 x intercept then its discrimiant must equal to zero.

    Remember that the discrimiant is the part under the radical in the quadratic formula

    B^2-4AC

    (-a)^2-4(1)(3-a)=0 \iff a^2+4a-12=0
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  3. #3
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    if it only intersects the x axis once, then there is only 1 solution. So the bit under the sqrt must be zero (since +0 = -0)

    edit i was too slow :P
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  4. #4
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    Ohh I see. Thank you very much
    But just for a clearer understanding for future problems. Why is it that when a parabola intersects only one point on the x-axis it means its discriminant = 0?
    Is this also true for horizontal axis parabolas when only hitting the y-axis once?
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  5. #5
    Super Member Quacky's Avatar
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    Think about how you solve a quadratic. Compare x^2+2x-24 (here) with x^2+2x+1 (here)

    Try and find the zeros of both with the quadratic formula, it should become clear.

    As for the horizontal axis parabolas, I can't see why it would be any different.
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  6. #6
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    I should revise my question. What does the discriminant mean for a parabola? Is it the focus coordinate? Is it where the parabola intersects with the axis?
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