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Math Help - tangent of a parabola

  1. #1
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    tangent of a parabola

    hi all pls all

    Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

    please solve the entire equation with explanation please. ty.
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  2. #2
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    Quote Originally Posted by andrew2322 View Post
    Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12
    please solve the entire equation with explanation please.
    The slope at each point on the parabola is 2x-1.
    Now why don't you show us what you have done on your own.
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  3. #3
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    \frac{dy}{dx}=2x-1

    Since the line is written in slop intercept form
    y=x+c we know that the slope of line is
    m=1

    Since we need the slope to equal the derivative we get...

    1=2x-1 solving for x we get

    x=1 This gives us half of the ordered pair...

    plugging this into the equation of the parabola we get

    y=(1)^2-(1)-12=-12 This completes our ordered pair giving us (1,-12)

    Now finally we use this ordered pair to solve for c plugging the ordered pair into the equation of the line we get....
    -12=1+C solving for C we finally end up with...

    y=x-13

    I hope this helps. Remember that the derivative represents the slope of the graph at any point.
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