Deck 9: Quadratic Equations

Question 1

Write standard form and identify $a, b$ , and $c$ .

- $\mathrm{x}^{2}+2 \mathrm{x}-5=0$

A) $x^{2}+2 x=5 ; a=1, b=2, c=5$
B) $x^{2}+2 x-5=0 ; a=1, b=-2, c=5$
C) $x^{2}+2 x-5=0 ; a=1, b=2, c=-5$
D) $x^{2}+2 x-5=0 ; a=0, b=2, c=-5$

Answer 1

$x^{2}+2 x-5=0 ; a=1, b=2, c=-5$

Question 2

Write standard form and identify $a, b$ , and $c$ .

- $5 x^{2}=4 x-4$

A) $5 x^{2}-4 x=-4 ; a=5, b=-4, c=-4$
B) $5 x^{2}+4 x+4=0 ; a=5, b=-4, c=-4$
C) $5 x^{2}+4 x-4=0 ; a=5, b=4, c=-4$
D) $5 x^{2}-4 x+4=0 ; a=5, b=-4, c=4$

Answer 2

$5 x^{2}-4 x+4=0 ; a=5, b=-4, c=4$

Question 3

Write standard form and identify $a, b$ , and $c$ .

- $7 x^{2}+1=-4 x-2$

A) $7 x^{2}+4 x+1=-2 ; a=7, b=4, c=1$
B) $7 \mathrm{x}^{2}-4 \mathrm{x}-3=0 ; \mathrm{a}=7, \mathrm{~b}=4, \mathrm{c}=-3$
C) $7 x^{2}+4 x+3=0 ; a=7, b=4, c=3$
D) $7 \mathrm{x}^{2}-4 \mathrm{x}+2=0 ; \mathrm{a}=7, \mathrm{~b}=-4, \mathrm{c}=2$

Answer 3

$7 x^{2}+4 x+3=0 ; a=7, b=4, c=3$

Question 4

Write standard form and identify $a, b$ , and $c$ .

- $-4=-3 x^{2}+5 x$

A) $3 x^{2}-5 x-4=0 ; a=3, b=-5, c=-4$
B) $-3 x^{2}+5 x+4 ; a=-3, b=5, c=4$
C) $3 x^{2}+5 x-4=0 ; a=3, b=5, c=-4$
D) $-3 x^{2}-5 x-4=0 ; a=3, b=-5, c=-4$

Question 5

Solve the equation.

- $6 m^{2}-12 m=0$

A) $0,-2$
B) 2, - 2
C) 0
D) 0,2

Question 6

Solve the equation.

- $49 n^{2}+14 n=0$

A) 0
B) $0,-\frac{2}{7}$
C) $0, \frac{2}{7}$
D) $\frac{2}{7},-\frac{2}{7}$

Question 7

Solve the equation.

- $8 r^{2}=2 r$

A) $\frac{1}{4}$
B) 0,4
C) $0, \frac{1}{4}$
D) 0

Question 8

Solve the equation.

- $7 y^{2}-3 y^{2}=42 y+9 y$

A) 0
B) - $\frac{51}{5}, \frac{51}{4}$
C) $0, \frac{51}{5}$
D) $0, \frac{51}{4}$

Question 9

Solve the equation.

- $x^{2}-x=56$

A) 7,8
B) $-7,-8$
C) 1,56
D) $-7,8$

Question 10

Solve the equation.

- $x^{2}+9 x-36=0$

A) $12,-3$
B) 12,3
C) $-12,1$
D) $-12,3$

Question 11

Solve the equation.

- $2 x^{2}-16 x+30=0$

A) 3,5
B) $0,3,5$
C) $-3,-5$
D) 2, 3, 5

Question 12

Solve the equation.

- $\mathrm{x}(\mathrm{x}-6)=55$

A) $5,-11$
B) 5,11
C) $-5,11$
D) $-5,-11$

Question 13

Solve the equation.

- $x^{2}-8 x+16=0$

A) 4
B) 3,5
C) -4
D) $0,-4$

Question 14

Solve the equation.

- $30 d^{2}+61 d+30=0$

A) $-\frac{5}{6},-\frac{6}{5}$
B) $\frac{6}{5}, \frac{5}{6}$
C) $\frac{5}{6}, \frac{6}{5}$
D) $-\frac{6}{5},-\frac{6}{5}$

Question 15

Solve the equation.

- $12 b^{2}+31 b+1=-19$

A) $-\frac{5}{4},-\frac{4}{3}$
B) $-\frac{4}{5},-\frac{4}{3}$
C) $\frac{4}{5}, \frac{3}{4}$
D) $\frac{5}{4}, \frac{4}{3}$

Question 16

Solve the equation.

- $6 k^{2}-53 k-9=0$

A) $\frac{1}{53},-\frac{1}{6}$
B) $-6,9$
C) $-\frac{1}{6}, 9$
D) $-\frac{1}{6}, 6$

Question 17

Solve the equation.

- $5 \mathrm{x}(\mathrm{x}+3)=(4 \mathrm{x}-5)(\mathrm{x}+3)$

A) $-3,-5$
B) -5
C) 3,5
D) 5

Question 18

Solve the equation.

- $\frac{24}{\mathrm{x}-2}+\frac{24}{\mathrm{x}+2}=5$

A) $-\frac{5}{2},-10$
B) 2,10
C) $-\frac{2}{5}, 10$
D) $\frac{2}{5},-10$

Question 19

Solve the equation.

- $\frac{\mathrm{m}}{\mathrm{m}-1}+\frac{23}{\mathrm{~m}^{2}-1}=\frac{13}{\mathrm{~m}+1}$

A) 7,5
B) 6, 6
C) $-6,-6$
D) 5, 7

Question 20

Solve the equation.

- $\frac{7-r}{r-7}+\frac{r+4}{r-4}=0$

A) No Solution
B) $-4,7$
C) 7,12
D) $-7,-12$

Question 21

Solve the equation.

- $\frac{5}{y+2}-\frac{7}{y-2}=\frac{8}{y^{2}-4}$

A) -16
B) 32
C) 16
D) $\sqrt{31}$

Question 22

Solve the equation.

- $\frac{9}{m-3}-\frac{8}{m+3}=\frac{8}{m^{2}-9}$

A) -43
B) $\sqrt{73}$
C) 43
D) No solution

Question 23

Solve the equation.

- $\frac{6}{m+4}-\frac{5}{m-4}=\frac{-48}{m^{2}-16}$

A) -4
B) No solution
C) 4
D) 6

Question 24

Solve the equation.

- $\frac{6}{m+5}=1-\frac{1}{m-5}$

A) $0,-5$
B) 0,7
C) 1,5
D) No solution

Question 25

Solve the problem.

-A polygon has 9 diagonals. How many sides does it have?

A) 6
B) 9
C) 5
D) 7

Question 26

Solve the problem.

-A polygon has 5 sides. How many diagonals does it have?

A) 8
B) 5
C) 6
D) 4

Question 27

Solve the equation. Express radicals in simplest form.

- $y^{2}=12$

A) $\sqrt{12}$
B) 6
C) $\pm \sqrt{12}$
D) 144

Question 28

Solve the equation. Express radicals in simplest form.

- $x^{2}=81$

A) 9
B) ±9
C) ± 10
D) 40.5

Question 29

Solve the equation. Express radicals in simplest form.

- $\mathrm{x}^{2}+2=102$

A)± 9
B) ± 10
C) 51
D) 10

Question 30

Solve the equation. Express radicals in simplest form.

- $2 x^{2}-392=0$

A) 14
B) ±15
C) ± 14
D) 197.5

Question 31

Solve the equation. Express radicals in simplest form.

- $-4 k^{2}-13=-77$

A) 4
B) ± 8
C) -38.5
D) ± 4

Question 32

Solve the equation. Express radicals in simplest form.

- $12 x^{2}-132=0$

A) ± 11
B) $\pm \sqrt{11}$
C) 11
D) 12

Question 33

Solve the equation. Express radicals in simplest form.

- $25 \mathrm{x}^{2}-9=0$

A) $\frac{5}{3}, 3$
B) $\frac{3}{5},-\frac{3}{5}$
C) $\frac{9}{25},-\frac{9}{25}$
D) $0, \frac{3}{5}$

Question 34

Solve the equation. Express radicals in simplest form.

- $(\mathrm{x}-4)^{2}=4$

A) $2,-2$
B) 2, -6
C) 8
D) 6,2

Question 35

Solve the equation. Express radicals in simplest form.

- $(r+5)^{2}=15$

A) $5+\sqrt{15}, 5-\sqrt{15}$
B) $\sqrt{15}, \sqrt{15}$
C) $-5+\sqrt{15},-5-\sqrt{15}$
D) 10

Question 36

Solve the equation. Express radicals in simplest form.

- $(x+8)^{2}=44$

A) $2 \sqrt{11},-2 \sqrt{11}$
B) $-8+2 \sqrt{22},-8-2 \sqrt{22}$
C) $2 \sqrt{11}-8,2 \sqrt{11}+8$
D) $-8+2 \sqrt{11},-8-2 \sqrt{11}$

Question 37

Solve the equation. Express radicals in simplest form.

- $(2 m-5)^{2}=49$

A) $1,-6$
B) $2,-12$
C) $12,-2$
D) $6,-1$

Question 38

Solve the equation. Express radicals in simplest form.

- $(4 \mathrm{x}+4)^{2}=64$

A) $1,-3$
B) 1,3
C) 0,1
D) $17,-17$

Question 39

Solve the equation. Express radicals in simplest form.

- $(3 \mathrm{x}+2)^{2}=6$

A) $\frac{-2 \pm \sqrt{6}}{3}$
B) $\frac{\sqrt{6} \pm 2}{3}$
C) $\frac{2 \pm \sqrt{6}}{3}$
D) $-\frac{8}{3}, \frac{4}{3}$

Question 40

Solve the equation. Express radicals in simplest form.

- $(5 \mathrm{z}-1)^{2}=\frac{4}{25}$

A) $\frac{2}{5},-\frac{2}{5}$
B) $\frac{7}{25}, \frac{3}{25}$
C) $3,-1$
D) $\frac{2}{25},-\frac{2}{25}$

Question 41

Solve the equation. Express radicals in simplest form.

- $(7-6 \mathrm{x})^{2}=2$

A) $\frac{7+\sqrt{2}}{6}, \frac{7-\sqrt{2}}{6}$

B) $\frac{-7+\sqrt{2}}{6}, \frac{-7-\sqrt{2}}{6}$

C) $\frac{-7-\sqrt{2}}{6}, \frac{7+\sqrt{2}}{6}$

D) $\frac{-7+\sqrt{2}}{6}, \frac{7-\sqrt{2}}{6}$

Question 42

Solve the equation. Express radicals in simplest form.

- $(x+4)^{2}-2=0$

A) $4 \pm \sqrt{2}$
B) $-2 \pm \sqrt{2}$
C) $-4 \pm \sqrt{2}$
D) $-2,6$

Question 43

Solve the equation. Express radicals in simplest form.

- $x^{2}+16 x+61=0$

A) $2+\sqrt{3}, 2-\sqrt{3}$
B) $-2+\sqrt{3},-2-\sqrt{3}$
C) $8+\sqrt{3}, 8-\sqrt{3}$
D) $-8+\sqrt{3},-8-\sqrt{3}$

Question 44

Solve the equation by completing the square.

- $\mathrm{a}^{2}+2 \mathrm{a}-24=0$

A) $-4,6$
B) $\sqrt{-24},-\sqrt{-24}$
C) $4,-6$
D) $-18,-6$

Question 45

Solve the equation by completing the square.

- $z^{2}+10 z+8=0$

A) $5+\sqrt{17}$
B) $5 \pm \sqrt{8}$
C) $5 \pm \sqrt{17}$
D) $-10+\sqrt{17}$

Question 46

Solve the equation by completing the square.

- $\mathrm{p}^{2}+3 \mathrm{p}-9=0$

A) $-3 \pm 3 \sqrt{5}$
B) $\frac{3+3 \sqrt{5}}{2}$
C) $\frac{-3-3 \sqrt{5}}{2}$
D) $\frac{-3 \pm 3 \sqrt{5}}{2}$

Question 47

Solve the equation by completing the square.

- $9 x^{2}+2 x-7=0$

A) $\frac{7}{9},-1$
B) $\frac{9}{7},-1$
C) $\frac{9}{7}, 0$
D) $\frac{9}{7}, 1$

Question 48

Solve the equation by completing the square.

- $12 \mathrm{~d}^{2}+40 \mathrm{~d}+25=0$

A) $-\frac{6}{5},-\frac{5}{2}$
B) $-\frac{5}{6},-\frac{5}{2}$
C) $\frac{5}{6}, \frac{5}{2}$
D) $\frac{6}{5}, \frac{2}{5}$

Question 49

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $2 m^{2}+10 m+7=0$

A) $\frac{-5 \pm \sqrt{11}}{2}$
B) $\frac{-10 \pm \sqrt{11}}{2}$
C) $\frac{-5 \pm \sqrt{11}}{4}$
D) $\frac{-5 \pm \sqrt{39}}{2}$

Question 50

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $3 \mathrm{n}^{2}=-10 \mathrm{n}-2$

A) $\frac{-5 \pm \sqrt{19}}{6}$
B) $\frac{-10 \pm \sqrt{19}}{3}$
C) $\frac{-5 \pm \sqrt{19}}{3}$
D) $\frac{-5 \pm \sqrt{31}}{3}$

Question 51

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $5 x^{2}+10 x=-4$

A) $\frac{-5 \pm \sqrt{5}}{5}$

B) $\frac{-10 \pm \sqrt{5}}{5}$ .

C) $\frac{-5 \pm \sqrt{5}}{5}$ .

D) $\frac{-5 \pm \sqrt{5}}{10}$

Question 52

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $x^{2}-x=42$

A) 6,7
B) $-6,-7$
C) 1,42
D) $-6,7$

Question 53

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $x^{2}+3 x-28=0$

A) $-7,1$
B) $7,-4$
C) 7,4
D) $-7,4$

Question 54

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $2 x^{2}-16 x+30=0$

A) $0,3,5$
B) 2, 3, 5
C) $-3,-5$
D) 3,5

Question 55

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $15 y^{2}+22 y+8=0$

A) $-\frac{4}{15},-\frac{1}{4}$
B) $\frac{4}{5}, \frac{2}{3}$
C) $-\frac{4}{5},-\frac{2}{3}$
D) $\frac{4}{5},-\frac{2}{3}$

Question 56

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $64 k^{2}-9=0$

A) $\frac{3}{8},-\frac{3}{8}$
B) 3,0
C) $\frac{8}{3},-\frac{8}{3}$
D) $\frac{8}{3}, 0$

Question 57

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $\frac{\mathrm{x}^{2}}{\mathrm{x}+3}-\frac{6}{\mathrm{x}+3}=0$

A) $-3, \sqrt{6}$
B) $-\sqrt{6}, \sqrt{6}$
C) $\sqrt{6}$
D) $-3,-\sqrt{6}, \sqrt{6}$

Question 58

Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula.

- $\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{x}+3}=\frac{1}{1}$

A) $\frac{-1 \pm \sqrt{21}}{2}$
B) $\frac{-5 \pm \sqrt{21}}{2}$
C) $\frac{5 \pm \sqrt{21}}{2}$
D) $\frac{1 \pm \sqrt{21}}{2}$

Question 59

Solve. Round results to the nearest thousandth.

- $x^{2}-8 x-7=0$

A) $0.796,-8.796$
B) $8.796,-0.796$
C) $8.500,-0.500$
D) $0.500,-8.500$

Question 60

Solve. Round results to the nearest thousandth.

- $9 \mathrm{x}^{2}-2 \mathrm{x}-18=0$

A) $1.307,-1.530$
B) $1.530,-1.307$
C) $1.217,-0.994$
D) $0.994,-1.217$

Question 61

Solve. Round results to the nearest thousandth.

- $x^{2}+9 x=-9$

A) $7.854,1.146$
B) $0.908,-9.908$
C) $-1.146,-7.854$
D) $-5.646,-5.646$

Question 62

Solve. Round results to the nearest thousandth.

- $2 \mathrm{x}^{2}-4 \mathrm{x}=-1$

A) $2.225,-0.225$
B) $-0.293,-1.707$
C) $3.414,0.586$
D) $1.707,0.293$

Question 63

Solve. Round results to the nearest thousandth.

- $5 y^{2}-5 y=1$

A) $2.342,-0.342$
B) $1.171,-0.171$
C) $0.171,-1.171$
D) $0.724,0.276$

Question 64

Solve. Round results to the nearest thousandth.

- $7 \mathrm{x}^{2}=4-2 \mathrm{x}$

A) $0.626,-0.912$
B) $0.885,-0.599$
C) $0.599,-0.885$
D) $0.912,-0.626$

Question 65

Solve for the specified variable.

- $\frac{1}{a}+\frac{1}{b}=c$ for $b$

A) $\frac{1}{\mathrm{ac}}$
B) $\frac{1}{\mathrm{C}}-\mathrm{a}$
C) ac $-\frac{1}{\mathrm{a}}$
D) $\frac{\mathrm{a}}{\mathrm{ac}-1}$

Question 66

Solve for the specified variable.

- $\frac{1}{a}+\frac{1}{b}=\frac{1}{C}$ for $c$

A) $a+b$
B) $\frac{a b}{a+b}$
C) $a b(a+b)$
D) $\frac{a+b}{a b}$

Question 67

Solve for the specified variable.

- $P=\frac{A}{1+r t}$ for $r$

A) $\frac{P-A}{1+t}$
B) $\frac{\mathrm{A}-\mathrm{P}}{\mathrm{Pt}}$
C) $\frac{\mathrm{P}-1}{\mathrm{At}}$
D) $\mathrm{P}$ - tA

Question 68

Solve for the specified variable.

- $\frac{P V}{T}=\frac{p v}{t}$ for $P$

A) $\frac{p v}{\text { tTV }}$
B) $\frac{\operatorname{tvT}}{\mathrm{pV}}$
C) $\frac{\mathrm{pvV}}{\mathrm{tT}}$
D) $\frac{\mathrm{pvT}}{\mathrm{tV}}$

Question 69

Solve for the specified variable.

- $I=\frac{E}{R+r}$ for $r$

A) $r=\frac{I R}{E}$
B) $r=\frac{E-I R}{I}$
C) $r=\frac{E-R}{I}$
D) $r=\frac{E}{I}-I R$

Question 70

Solve for the specified variable.

- $I=\frac{k E}{R}$ for $R$

A) $\mathrm{R}=\mathrm{kEI}$
B) $\mathrm{R}=\frac{\mathrm{kE}}{\mathrm{I}}$
C) $\mathrm{R}=\mathrm{kE}-\mathrm{I}$
D) $\mathrm{R}=\frac{\mathrm{I}}{\mathrm{kE}}$

Question 71

Solve for the specified variable.

- $S=\frac{a}{1-r}$ for $r$

A) $r=\frac{S-a}{S}$
B) $r=\frac{a}{S}-1$
C) $r=\frac{a}{S}$
D) $r=S-a$

Question 72

Solve for the specified variable.

- $2 x+\frac{3}{z}=\frac{5}{y}$ for $z$

A) $z=\frac{-3 y}{2 x-5}$
B) $z=\frac{3 y}{5-2 x}$
C) $z=\frac{-3 y}{2 x y-5}$
D) $z=\frac{5-2 x y}{3 y}$

Question 73

Solve the formula for the specified variable.

- $M=\pi r^{2} h d$ for $r$

A) $r= \pm \sqrt{\pi \text { Mhd }}$
B) $r=\frac{ \pm \sqrt{\mathrm{M} \pi \mathrm{hd}}}{\pi \mathrm{hd}}$
C) $r=\frac{ \pm \sqrt{\pi \mathrm{Mhd}}}{\text { hd }}$
D) $r=\frac{ \pm M \sqrt{\pi h d}}{\pi h d}$

Question 74

Solve the formula for the specified variable.

- $\mathrm{A}=3 \pi \mathrm{a}^{2}$ for $\mathrm{a}$

A) $a=\frac{ \pm \sqrt{3 \pi \mathrm{A}}}{3 \pi}$
B) $\mathrm{a}=\frac{ \pm \mathrm{A} \sqrt{3 \pi}}{3 \pi}$
C) $a=\frac{ \pm \sqrt{\mathrm{A} \pi}}{3}$
D) $a=\sqrt{3 \pi \mathrm{A}}$

Question 75

Solve the formula for the specified variable.

- $\mathrm{Ve}=\frac{1}{2} \mathrm{mv}^{2}$ for $v$

A) $v= \pm \sqrt{\frac{V e}{2 m}}$
B) $v= \pm 2 \frac{\sqrt{\mathrm{Ve}}}{\mathrm{m}}$
C) $v=\frac{ \pm \sqrt{2 m V e}}{m}$
D) $v= \pm \sqrt{2 \mathrm{Ve}}$

Question 76

Solve the formula for the specified variable.

- $v=\sqrt{\frac{2 g E}{m}}$ , for $E$

A) $E=\frac{v^{2} m}{2 g}$
B) $E=\frac{v^{2} m}{g}$
C) $E=\frac{v^{2} m}{4 g}$
D) $E=\frac{v m}{2 g}$

Question 77

Solve the formula for the specified variable.

- $c=\sqrt{a^{2}+b^{2}}$ for $b$

A) $b=\sqrt{c^{2}-a^{2}}$
B) $b=\sqrt{a^{2}-c^{2}}$
C) $b=\sqrt{b^{2}-c^{2}}$
D) $b=\sqrt{c^{2}-b^{2}}$

Question 78

Solve the formula for the specified variable.

- $h=\frac{a}{2} \sqrt{3}$ for $a$

A) $a=\frac{\sqrt{3}}{3} h$
B) $a=\frac{\sqrt{3}}{2} h$
C) $a=\frac{2 \sqrt{3}}{3 h}$
D) $a=\frac{2 \sqrt{3}}{3} h$

Question 79

Solve for the indicated letter.

-Solve the formula $S=\frac{1}{3} \pi r^{2} h+4 \pi r h$ for $r$ .

A) $r=\frac{12 \pi h \pm \sqrt{36 \pi^{2} h^{2}+3 \pi h S}}{\pi h}$
B) $r=\frac{-6 \pi h \pm \sqrt{36 \pi^{2} h^{2}+3 \pi h S}}{\pi h}$
C) $r=\frac{-6 \pi h \pm 2 \sqrt{36 \pi^{2} h^{2}+3 \pi h S}}{\pi h}$
D) $r=\frac{-12 \pi \mathrm{h} \pm \sqrt{36 \pi^{2} \mathrm{~h}^{2}+3 \pi \mathrm{hS}}}{2 \pi \mathrm{h}}$

Question 80

Solve for the indicated letter.

-Solve $S=x^{2}+y^{2}-8 x+10 y-4$ for $x$ .

A) $x=4 \pm \sqrt{68-y^{2}-10 y+S}$
B) $x=4 \pm \sqrt{16-y^{2}-10 y+S}$
C) $x=4 \pm \sqrt{12-y^{2}-10 y-S}$
D) $x=4 \pm \sqrt{20-y^{2}-10 y+S}$