Sample quiz on completing the square
Main home here.

  1. What value of $c$ will make the quadratic $x^2+6x+c$ a perfect square?
    $36$
    $16$
    $9$
    $4$.
  2. What value of $c$ will make the quadratic $x^2+4x+c$ a perfect square?
    $1$
    $4$
    $8$
    $16$
  3. What value of $c$ will make the quadratic $x^2-8x+c$ a perfect square?
    $4$
    $8$
    $16$
    $64$
  4. Complete the square for $x^2-8x+1$.
    $(x+4)^2-15$
    $(x-8)^2-15$
    $(x-4)^2-15$
    $(x-4)^2+15$
  5. Write $x^2+6x+9$ as a perfect square.
    $(x-3)^2$
    $(x+6)^2$
    $(x+9)^2$
    $(x+3)^2$
  6. Write $25x^2+10x+1$ as a perfect square.
    $(5x+1)^2$
    $(5x-1)^2$
    $(5+x)^2$
    $(25x+1)^2$
  7. Write $36x^2-60x+25$ as a perfect square.
    $(6x-5)^2$
    $(6x+5)^2$
    $(6+5x)^2$
    $(6-5x)^2$
  8. Complete the square in $x^2-4x-2$.
    $(x+2)^2-6$
    $(x-2)^2-6$
    $(x-2)^2+6$
    $(x-4)^2-6$
  9. Complete the square in $2x^2+4x+1$.
    $2(x+1)^2+1$
    $2(x-1)^2-1$
    $2(x+1)^2-2$
    $2(x+1)^2-1$
  10. Complete the square in $-x^2+2x+3$.
    $-(x-1)^2-2$
    $-(x+1)^2+4$
    $-(x-1)^2+4$
    $-(x-2)^2+2$
  11. Complete the square for $-2x^2+8x-3$.
    $-2(x-2)^2-11$
    $-2(x-2)^2+11$
    $-2(x-4)^2+5$
    $-2(x-2)^2+5$
  12. Find the vertex of the quadratic $3x^2+12x+1$.
    $(-2,-11)$
    $(-2,-13)$
    $(-2,-3)$
    $(2,-11)$
  13. Find the vertex of the quadratic $-5x^2+20x-3$
    $(2,-23)$
    $(2,-17)$
    $(2,17)$
    $(4,17)$
  14. Complete the square for $x^2+x+1$.
    $\Big(x+\frac{1}{4}\Big)^2+\frac{3}{4}$
    $\Big(x-\frac{1}{2}\Big)^2+\frac{3}{4}$
    $\Big(x+\frac{1}{2}\Big)^2-\frac{3}{4}$
    $\Big(x+\frac{1}{2}\Big)^2+\frac{3}{4}$
  15. Complete the square for $-x^2+3x-5$.
    $-\Big(x-\frac{3}{2}\Big)^2+\frac{11}{4}$
    $-\Big(x-\frac{3}{2}\Big)^2-\frac{29}{4}$
    $-\Big(x-\frac{3}{2}\Big)^2-\frac{11}{4}$
    $-\Big(x+\frac{3}{2}\Big)^2-\frac{11}{4}$
  16. Find the vertex of the quadratic $5x^2+x-3$
    $\Big(-\frac{1}{10},-\frac{61}{10}\Big)$
    $\Big(-\frac{1}{10},-\frac{63}{20}\Big)$
    $\Big(-\frac{1}{10},-\frac{61}{20}\Big)$
    $\Big(-\frac{1}{5},-\frac{61}{20}\Big)$
  17. If $3x^2-7x+9$ is written in the form $a(x-h)^2+k$, determine the values of $a,h,k$
    $a=3,h=\frac{7}{6},h=\frac{95}{12}$
    $a=3,h=\frac{7}{3},h=\frac{59}{12}$
    $a=3,h=\frac{7}{12},h=\frac{59}{12}$
    $a=3,h=\frac{7}{6},h=\frac{59}{12}$
  18. If $3x^2-18x+27$ is written in the form $a(x-h)^2+k$, determine the values of $a,h,k$
    $a=3,h=3,k=9$
    $a=3,h=3,k=0$
    $a=3,h=6,k=9$
    $a=3,h=-3,k=0$
  19. Find the minimum value of the quadratic $3x^2+4x+5$
    $\frac{11}{6}$
    $\frac{22}{3}$
    $\frac{11}{12}$
    $\frac{11}{3}$
  20. Which of the following quadratics has the smallest minimum value?
    $x^2+x+1$
    $x^2+2x+1$
    $x^2-2x-1$
    $x^2+x+2$