Deck 15: Quadratic Equations

Question 1

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

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

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

Answer 1

$x^{2}+2 x-3=0 ; a=1, b=2, c=-3$

Question 2

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

- $6 x^{2}=3 x+1$

A) $6 x^{2}-3 x=1 ; a=6, b=-3, c=1$
B) $6 x^{2}+3 x-1=0 ; a=6, b=-3, c=1$
C) $6 x^{2}+3 x+1=0 ; a=6, b=3, c=1$
D) $6 x^{2}-3 x-1=0 ; a=6, b=-3, c=-1$

Answer 2

$6 x^{2}-3 x-1=0 ; a=6, b=-3, c=-1$

Question 3

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

- $2 x^{2}-3=4 x-1$

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

Answer 3

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

Question 4

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

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

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

Question 5

Solve the equation.

- $12 m^{2}-24 m=0$

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

Question 6

Solve the equation.

- $10 n^{2}+18 n=0$

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

Question 7

Solve the equation.

- $8 r^{2}=4 r$

A) 0
B) 0,2
C) $0, \frac{1}{2}$
D) $\frac{1}{2}$

Question 8

Solve the equation.

- $7 y^{2}-2 y^{2}=44 y+7 y$

A) $0, \frac{57}{5}$
B) 0
C) $0, \frac{51}{5}$
D) $-\frac{57}{5}, \frac{51}{5}$

Question 9

Solve the equation.

- $x^{2}-x=72$

A) $-8,-9$
B) 8,9
C) 1,72
D) $-8,9$

Question 10

Solve the equation.

- $x^{2}+7 x-30=0$

A) $10,-3$
B) 10,3
C) $-10,3$
D) $-10,1$

Question 11

Solve the equation.

- $4 x^{2}-28 x+40=0$

A) $-2,-5$
B) $4,2,5$
C) $0,2,5$
D) 2,5

Question 12

Solve the equation.

- $x(x-1)=42$

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

Question 13

Solve the equation.

- $x^{2}+10 x+25=0$

A) 0,5
B) $-6,-4$
C) -5
D) 5

Question 14

Solve the equation.

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

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

Question 15

Solve the equation.

- $30 b^{2}+43 b-2=-17$

A) $-\frac{5}{3},-\frac{5}{6}$
B) $\frac{5}{3}, \frac{6}{5}$
C) $\frac{3}{5}, \frac{5}{6}$
D) $-\frac{3}{5},-\frac{5}{6}$

Question 16

Solve the equation.

- $4 \mathrm{k}^{2}-31 \mathrm{k}-8=0$

A) $-\frac{1}{4}, 8$
B) $\frac{1}{31},-\frac{1}{4}$
C) $-4,8$
D) $-\frac{1}{4}, 4$

Question 17

Solve the equation.

- $5 x(x+2)=(4 x-6)(x+2)$

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

Question 18

Solve the equation.

- $\frac{15}{x-2}+\frac{15}{x+2}=4$

A) $-2,-8$
B) $-\frac{1}{2}, 8$
C) 2, 8
D) $\frac{1}{2},-8$

Question 19

Solve the equation.

- $\frac{m}{m-1}+\frac{14}{m^{2}-1}=\frac{11}{m+1}$

A) 4,6
B) 6,4
C) $-5,-5$
D) 5, 5

Question 20

Solve the equation.

- $\frac{7-r}{r-7}+\frac{r+3}{r-3}=0$

A) 7,9
B) $-3,7$
C) $-7,-9$
D) No Solution

Question 21

Solve the equation.

- $\frac{1}{y+2}-\frac{3}{y-2}=\frac{6}{y^{2}-4}$

A) $\sqrt{1}$
B) -7
C) 14
D) 7

Question 22

Solve the equation.

- $\frac{4}{m-5}-\frac{7}{m+5}=\frac{7}{m^{2}-25}$

A) 16
B) No solution
C) -16
D) $\sqrt{46}$

Question 23

Solve the equation.

- $\frac{7}{m+4}-\frac{6}{m-4}=\frac{-56}{m^{2}-16}$

A) -4
B) 4
C) 7
D) No solution

Question 24

Solve the equation.

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

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

Question 25

Solve the problem.

-A polygon has 27 diagonals. How many sides does it have?

A) 8
B) 9
C) 10
D) 12

Question 26

Solve the problem.

-A polygon has 8 sides. How many diagonals does it have?

A) 20
B) 11
C) 7
D) 9

Question 27

Solve the equation. Express radicals in simplest form.

- $y^{2}=2$

A) $\sqrt{2}$
B) $\pm \sqrt{2}$
C) 1
D) 4

Question 28

Solve the equation. Express radicals in simplest form.

- $x^{2}=25$

A) 12.5
B) 5
C) $\pm 6$
D) $\pm 5$

Question 29

Solve the equation. Express radicals in simplest form.

- $\mathrm{x}^{2}+2=18$

A) $\pm 3$
B) 9
C) $\pm 4$
D) 4

Question 30

Solve the equation. Express radicals in simplest form.

- $5 x^{2}-20=0$

A) 12
B) $\pm 2$
C) $\pm 3$
D) 2

Question 31

Solve the equation. Express radicals in simplest form.

- $-2 k^{2}-1=-19$

A) $\pm 3$
B) $\pm 6$
C) 3
D) -9.5

Question 32

Solve the equation. Express radicals in simplest form.

- $8 x^{2}-56=0$

A) $\pm 7$
B) 7
C) 8
D) $\pm \sqrt{7}$

Question 33

Solve the equation. Express radicals in simplest form.

- $9 x^{2}-81=0$

A) 0,3
B) $\frac{1}{3}, 9$
C) $9,-9$
D) $3,-3$

Question 34

Solve the equation. Express radicals in simplest form.

- $(x-6)^{2}=49$

A) $7,-7$
B) $13,-1$
C) 55
D) $-1,-13$

Question 35

Solve the equation. Express radicals in simplest form.

- $(r+5)^{2}=17$

A) $-5+\sqrt{17},-5-\sqrt{17}$
B) 12
C) $5+\sqrt{17}, 5-\sqrt{17}$
D) $\sqrt{17}, \sqrt{17}$

Question 36

Solve the equation. Express radicals in simplest form.

- $(x+2)^{2}=12$

A) $-2+2 \sqrt{6},-2-2 \sqrt{6}$
B) $2 \sqrt{3},-2 \sqrt{3}$
C) $-2+2 \sqrt{3},-2-2 \sqrt{3}$
D) $2 \sqrt{3}-2,2 \sqrt{3}+2$

Question 37

Solve the equation. Express radicals in simplest form.

- $(2 m-5)^{2}=25$

A) $0,-10$
B) 10,0
C) $0,-5$
D) 5,0

Question 38

Solve the equation. Express radicals in simplest form.

- $(2 x+2)^{2}=16$

A) $9,-9$
B) 1,3
C) 0,1
D) $1,-3$

Question 39

Solve the equation. Express radicals in simplest form.

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

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

Question 40

Solve the equation. Express radicals in simplest form.

- $(3 \mathrm{z}-1)^{2}=\frac{4}{9}$

A) $\frac{2}{3},-\frac{2}{3}$
B) $\frac{2}{9},-\frac{2}{9}$
C) $3,-1$
D) $\frac{5}{9}, \frac{1}{9}$

Question 41

Solve the equation. Express radicals in simplest form.

- $(7-5 x)^{2}=2$

A) $\frac{-7+\sqrt{2}}{5}, \frac{7-\sqrt{2}}{5}$
B) $\frac{-7-\sqrt{2}}{5}, \frac{7+\sqrt{2}}{5}$
C) $\frac{-7+\sqrt{2}}{5}, \frac{-7-\sqrt{2}}{5}$
D) $\frac{7+\sqrt{2}}{5}, \frac{7-\sqrt{2}}{5}$

Question 42

Solve the equation. Express radicals in simplest form.

- $(x+16)^{2}-2=0$

A) $-16 \pm \sqrt{2}$
B) $16 \pm \sqrt{2}$
C) $-4 \pm \sqrt{2}$
D) $-14,18$

Question 43

Solve the equation. Express radicals in simplest form.

- $x^{2}+16 x+62=0$

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

Question 44

Solve the equation by completing the square.

- $\mathrm{a}^{2}-4 \mathrm{a}-21=0$

A) $7,-3$
B) $\sqrt{-21},-\sqrt{-21}$
C) $-18,-3$
D) $-7,3$

Question 45

Solve the equation by completing the square.

- $z^{2}+10 z+4=0$

A) $5 \pm \sqrt{4}$
B) $5 \pm \sqrt{21}$
C) $5+\sqrt{21}$
D) $-10+\sqrt{21}$

Question 46

Solve the equation by completing the square.

- $\mathrm{p}^{2}+4 \mathrm{p}-4=0$

A) $\frac{-4-4 \sqrt{2}}{2}$
B) $-4 \pm 4 \sqrt{2}$
C) $\frac{4+4 \sqrt{2}}{2}$
D) $\frac{-4 \pm 4 \sqrt{2}}{2}$

Question 47

Solve the equation by completing the square.

- $15 \mathrm{~d}^{2}+43 \mathrm{~d}+30=0$

A) $-\frac{5}{3},-\frac{6}{5}$
B) $\frac{5}{3}, \frac{6}{5}$
C) $\frac{3}{5}, \frac{5}{6}$
D) $-\frac{3}{5},-\frac{6}{5}$

Question 48

Solve the problem. Round to the nearest tenth, if necessary.

-A rock falls from a tower that is 480 feet high. As it is falling, its height is given by the formula $\mathrm{h}=480-16 \mathrm{t}^{2}$ . How many seconds will it take for the rock to hit the ground $(\mathrm{h}=0)$ ?

A) $14,400 \mathrm{sec}$
B) $21.9 \mathrm{sec}$
C) $21.5 \mathrm{sec}$
D) $5.5 \mathrm{sec}$

Question 49

Solve the problem. Round to the nearest tenth, if necessary.

-A rock falls from a tower that is $63.7 \mathrm{~m}$ high. As it is falling, its height is given by the formula $\mathrm{h}=63.7-4.9 \mathrm{t}^{2}$ . How many seconds will it take for the rock to hit the ground $(\mathrm{h}=0)$ ?

A) $8 \mathrm{sec}$
B) $7.7 \mathrm{sec}$
C) $3.6 \mathrm{sec}$
D) $828.1 \mathrm{sec}$

Question 50

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

- $2 m^{2}+6 m+3=0$

A) $\frac{-3 \pm \sqrt{3}}{4}$
B) $\frac{-3 \pm \sqrt{3}}{2}$
C) $\frac{-3 \pm \sqrt{15}}{2}$
D) $\frac{-6 \pm \sqrt{3}}{2}$

Question 51

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

- $6 n^{2}=-10 n-3$

A) $\frac{-5 \pm \sqrt{43}}{6}$
B) $\frac{-10 \pm \sqrt{7}}{6}$
C) $\frac{-5 \pm \sqrt{7}}{6}$
D) $\frac{-5 \pm \sqrt{7}}{12}$

Question 52

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

- $5 x^{2}+12 x=-6$

A) $\frac{-12 \pm \sqrt{6}}{5}$
B) $\frac{-6 \pm \sqrt{6}}{5}$
C) $\frac{-6 \pm \sqrt{66}}{5}$
D) $\frac{-6 \pm \sqrt{6}}{10}$

Question 53

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

- $x^{2}-x=6$

A) $-2,-3$
B) 2,3
C) $-2,3$
D) 1, 6

Question 54

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

- $x^{2}+9 x-22=0$

A) $-11,2$
B) $-11,1$
C) 11,2
D) $11,-2$

Question 55

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

- $2 x^{2}-14 x+24=0$

A) $0,3,4$
B) 2,3,4
C) $-3,-4$
D) 3,4

Question 56

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

- $15 y^{2}+19 y+6=0$

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

Question 57

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

- $25 \mathrm{k}^{2}-81=0$

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

Question 58

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

- $\frac{x^{2}}{x-2}-\frac{12}{x-2}=0$

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

Question 59

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

- $\frac{1}{x}+\frac{1}{x+3}=\frac{1}{2}$

A) $\frac{7 \pm \sqrt{29}}{2}$
B) $\frac{-1 \pm \sqrt{29}}{2}$
C) $\frac{1 \pm \sqrt{29}}{2}$
D) $\frac{-7 \pm \sqrt{29}}{2}$

Question 60

Solve. Round results to the nearest thousandth.

- $x^{2}+8 x-32=0$

A) $2.928,-10.928$
B) $19.748,-11.748$
C) $11.748,-19.748$
D) $10.928,-2.928$

Question 61

Solve. Round results to the nearest thousandth.

- $2 x^{2}+8 x+1=0$

A) $3.984,0.016$
B) $3.871,0.129$
C) $-0.016,-3.984$
D) $-0.129,-3.871$

Question 62

Solve. Round results to the nearest thousandth.

- $x^{2}+6 x=-8$

A) $4.000,2.000$
B) $1.123,-7.123$
C) $-5.000,-5.000$
D) $-2.000,-4.000$

Question 63

Solve. Round results to the nearest thousandth.

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

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

Question 64

Solve. Round results to the nearest thousandth.

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

A) $-0.276,-0.724$
B) $0.724,0.276$
C) $1.448,0.552$
D) $1.171,-0.171$

Question 65

Solve. Round results to the nearest thousandth.

- $9 x^{2}=6+10 x$

A) $0.043,-1.154$
B) $0.432,-1.543$
C) $1.154,-0.043$
D) $1.543,-0.432$

Question 66

Solve for the specified variable.

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

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

Question 67

Solve for the specified variable.

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

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

Question 68

Solve for the specified variable.

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

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

Question 69

Solve for the specified variable.

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

A) $\frac{\mathrm{tvT}}{\mathrm{pV}}$
B) $\frac{\mathrm{pvV}}{\mathrm{tT}}$
C) $\frac{\mathrm{pvT}}{\mathrm{tV}}$
D) $\frac{\mathrm{pv}}{\mathrm{tTV}}$

Question 70

Solve for the specified variable.

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

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

Question 71

Solve for the specified variable.

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

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

Question 72

Solve for the specified variable.

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

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

Question 73

Solve for the specified variable.

- $7 x+\frac{5}{z}=\frac{3}{y}$ for $z$

A) $z=\frac{-5 y}{7 x y-3}$
B) $z=\frac{3-7 x y}{5 y}$
C) $z=\frac{5 y}{3-7 x}$
D) $z=\frac{-5 y}{7 x-3}$

Question 74

Solve the formula for the specified variable.

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

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

Question 75

Solve the formula for the specified variable.

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

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

Question 76

Solve the formula for the specified variable.

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

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

Question 77

Solve the formula for the specified variable.

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

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

Question 78

Solve the formula for the specified variable.

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

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

Question 79

Solve the formula for the specified variable.

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

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

Question 80

Solve for the indicated letter.

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

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