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Quiz 1

Mathematics Department
Tennessee Technological University


Date: July 18, 2018


  1. Find the quotient $ q(x)$ and the remainder $ r$ in the division of $ \displaystyle 3\,x^5-7\,x^2+2$ by x − 2, and express them in the form of (x − 2)q(x) + r.

    $ \displaystyle \left(x-2\right)\,\left(3\,x^4+6\,x^3+12\,x^2+17\,x+34\right)-70$

    $ \displaystyle \left(x-2\right)\,\left(3\,x^4-6\,x^3+12\,x^2-31\,x+62\right)-122$

    $ \displaystyle \left(x-2\right)\,\left(3\,x^4+6\,x^3+12\,x^2+17\,x+34\right)+70$

    $ \displaystyle \left(x-2\right)\,\left(3\,x^4-6\,x^3+12\,x^2-31\,x+62\right)+122$

  2. Sketch the graph of $ \displaystyle 4\,x-x^2$.

    \includegraphics{thisquiz_pick_plot0.ps}

    \includegraphics{thisquiz_pick_plot1.ps}

    \includegraphics{thisquiz_pick_plot2.ps}

    \includegraphics{thisquiz_pick_plot3.ps}

  3. Find the vertex of $ \displaystyle -x^2+4\,x-3$.

    [ 2 ,  1 ]

    [  − 2 ,   − 1 ]

    [  − 2 ,  1 ]

    [ 2 ,   − 1 ]

  4. Solve the equation $ \displaystyle 3\,x^2-7\,x-3=0$.

    $ \displaystyle \left[ x=-{{\sqrt{85}+7}\over{6}} , x={{\sqrt{85}-7}\over{6}}
\right] $

    $ \displaystyle \left[ x=-{{\sqrt{13}-7}\over{6}} , x={{\sqrt{13}+7}\over{6}}
\right] $

    $ \displaystyle \left[ x=-{{\sqrt{85}-7}\over{6}} , x={{\sqrt{85}+7}\over{6}}
\right] $

    $ \displaystyle \left[ x=-{{\sqrt{61}-7}\over{2}} , x={{\sqrt{61}+7}\over{2}}
\right] $

  5. Find the equation for the parabola shown below.

    \includegraphics{thisquiz_pick_plot4.ps}

    $ \displaystyle y=-2\,x^2+2\,x+12$

    $ \displaystyle y=x^2-x-6$

    $ \displaystyle y=2\,x^2-2\,x-12$

    $ \displaystyle y=-x^2+x+6$

  6. If a linear function $ f$ satisfies 0 = 1 and 4 = −1, find $ f(x)$.

    y = x

    y = x

    y = x

    y = x

  7. Sketch the graph of $ \displaystyle {{x^3}\over{2}}+x^2-{{3\,x}\over{2}}$.

    \includegraphics{thisquiz_pick_plot5.ps}

    \includegraphics{thisquiz_pick_plot6.ps}

    \includegraphics{thisquiz_pick_plot7.ps}

    \includegraphics{thisquiz_pick_plot8.ps}

  8. Find the polynomial function of degree $ 3$ in the graph below.

    \includegraphics{thisquiz_pick_plot9.ps}

    $ \displaystyle y=x^3-2\,x^2-4\,x+8$

    $ \displaystyle y=-x^3+2\,x^2+4\,x-8$

    $ \displaystyle y=x^3+2\,x^2-4\,x-8$

    $ \displaystyle y=-x^3-2\,x^2+4\,x+8$





Department of Mathematics
Last modified: 2018-07-18