# 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?
$x^2+x+1$
$x^2+2x+1$
$x^2-2x-1$
$x^2+x+2$