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

    [ 2 ,  4 ]

    [  − 2 ,  4 ]

    [ 2 ,   − 4 ]

    [  − 2 ,   − 4 ]

  2. If a linear function $f$ satisfies f(1) = 5 and f( − 1) = 10, find $f(x)$.

    $\displaystyle y=-{{5\,x}\over{2}}-{{15}\over{2}}$

    $\displaystyle y={{15}\over{2}}-{{5\,x}\over{2}}$

    y = 5x + 15

    y = 5x − 15

  3. Solve the equation $\displaystyle \ln x=\ln \left(x+1\right)-2$

    $\displaystyle \left[ x=-{{e^2}\over{e^2-1}} \right] $

    [ x = 1 ]

    $\displaystyle \left[ x={{1}\over{e^2-1}} \right] $

    [ x = −1 ]

  4. Sketch the graph of $\displaystyle y=\sqrt{x-3}+4$ .

    Image s20quiz01_pick_plot0

    Image s20quiz01_pick_plot1

    Image s20quiz01_pick_plot2

    Image s20quiz01_pick_plot3

  5. Sketch the graph for

    $\displaystyle f(x) = \begin{cases} x-1 & \mbox{if $x < 1$} \\ -x^2 & \mbox{if $ 1 \le x \le 4$} \\ 3-x & \mbox{if $ 4 < x$} \end{cases} $

    Image s20quiz01_pick_plot4

    Image s20quiz01_pick_plot5

    Image s20quiz01_pick_plot6

    Image s20quiz01_pick_plot7

  6. Solve the equation $\displaystyle 4^{x}\,2^{x+1} = ( {{1}\over{2}}) 2^{2\,x}$

    $\displaystyle \left[ x=-{{1}\over{2}} \right] $

    [ x = 2 ]

    $\displaystyle \left[ x=-{{1}\over{6}} \right] $

    [ x = −2 ]

  7. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot8

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

    $\displaystyle y=-{{x^2}\over{2}}+2\,x-{{3}\over{2}}$

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

    $\displaystyle y={{x^2}\over{2}}-2\,x+{{3}\over{2}}$

  8. Solve the equation $\displaystyle 2^{x}=7^{1-x}$

    [ x = 1 ]

    $\displaystyle \left[ x={{1}\over{2}} \right] $

    $\displaystyle \left[ x={{\ln 7}\over{\ln 7+\ln 2}} \right] $

    $\displaystyle \left[ x={{1}\over{\ln 7+\ln 2}} \right] $

  9. Solve the equation $\displaystyle 2^{x-5}=8$

    [ x = 13 ]

    [ x = −2 ]

    [ x = 256 ]

    [ x = 8 ]

  10. Solve the equation $\displaystyle -2\,x^2+4\,x+1=0$.

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

    $\displaystyle \left[ x=-{{\sqrt{6}-2}\over{2}} , x={{\sqrt{6}+2}\over{2}} \right] $

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

    $\displaystyle \left[ x=-{{\sqrt{6}+2}\over{2}} , x={{\sqrt{6}-2}\over{2}} \right] $


Department of Mathematics
Last modified: 2026-01-17