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Math Help - Two really easy graph problems

  1. #1
    Junior Member
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    Two really easy graph problems

    I seem to be missing something really easy step or something.


    On a separate piece of paper, sketch the graph of the parabola . On the same graph, plot the point . Note that there are two tangent lines of that pass through the point .
    Specifically, the tangent line of the parabola at the point passes through the point where . The other tangent line that passes through the point occurs at the point .

    Find the number a=

    Thanks!
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Here is what we know.

    The slope between two points is given by

    m=\frac{y_2-y_1}{x_2-x_1}

    also the slope at a point is the derivative evaluated at that point.

    Using the above we get and the points (a,a^2+4);(0,-2)

    m=\frac{a^2+4-(-2)}{a-0}=\frac{a^2+6}{a}

    the derivative at that point is

    y'=2x \implies m=2a

    Now set them equal and solve for a

    2a=\frac{a^2+6}{a}
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