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Quiz 1

Mathematics Department
Tennessee Technological University


Date: December 13, 2017


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

    \includegraphics{thisquiz_pick_plot0.ps}

    \includegraphics{thisquiz_pick_plot1.ps}

    \includegraphics{thisquiz_pick_plot2.ps}

    \includegraphics{thisquiz_pick_plot3.ps}

  2. Solve the equation $ \displaystyle 2\,x^2+6\,x+4=0$.

    [ x = 1 ,  x = 2 ]

    $ \displaystyle \left[ x=-{{\sqrt{17}+3}\over{2}} , x={{\sqrt{17}-3}\over{2}}
\right] $

    [ x = −2 ,  x =  − 1 ]

    $ \displaystyle \left[ x=-\sqrt{5}-3 , x=\sqrt{5}-3 \right] $

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

    [  − 2 ,  1 ]

    [  − 2 ,   − 1 ]

    [ 2 ,  1 ]

    [ 2 ,   − 1 ]

  4. If a linear function $ f$ satisfies f(1) = 3 and f( − 1) = 8, find $ f(x)$.

    y = 3x + 11

    $ \displaystyle y=-{{5\,x}\over{2}}-{{11}\over{2}}$

    $ \displaystyle y={{11}\over{2}}-{{5\,x}\over{2}}$

    y = 3x − 11

  5. Find the quotient $ q(x)$ and the remainder $ r$ in the division of $ \displaystyle -2\,x^5-5\,x^2+4$ by x − 2, and express them in the form of (x − 2)q(x) + r.

    $ \displaystyle \left(x-2\right)\,\left(-2\,x^4-4\,x^3-8\,x^2-21\,x-42\right)+80$

    $ \displaystyle \left(x-2\right)\,\left(-2\,x^4-4\,x^3-8\,x^2-21\,x-42\right)-80$

    $ \displaystyle \left(x-2\right)\,\left(-2\,x^4+4\,x^3-8\,x^2+11\,x-22\right)+48$

    $ \displaystyle \left(x-2\right)\,\left(-2\,x^4+4\,x^3-8\,x^2+11\,x-22\right)-48$

  6. Find the equation for the parabola shown below.

    \includegraphics{thisquiz_pick_plot4.ps}

    $ \displaystyle y=2\,x^2-8\,x+6$

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

    $ \displaystyle y=-2\,x^2+8\,x-6$

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

  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: 2017-12-13