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Thread: Two really easy graph problems

  1. #1
    Junior Member
    Jul 2010

    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=

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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Feb 2008
    Yuma, AZ, USA
    Here is what we know.

    The slope between two points is given by

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

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

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

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

    the derivative at that point is

    $\displaystyle y'=2x \implies m=2a$

    Now set them equal and solve for a

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