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SOLVING QUADRATICS REVIEW

Total questions: 36

Worksheet time: 19mins

Name
Class
Date
1.

Simplify  384\sqrt{384}  

a)

3 7\sqrt{7}  

b)

6 5\sqrt{5}  

c)

8 6\sqrt{6}  

d)

2 3\sqrt{3}  

2.

 128\sqrt{128}  Simplify

a)

2 7\sqrt{7}  

b)

8 2\sqrt{2}  

c)

8

d)

6 2\sqrt{2}  

3.

 94−2i\frac{9}{4-2i}  Simplify

a)

 14+7i10\frac{14+7i}{10}  

b)

 18+9i10\frac{18+9i}{10}  

c)

 12+6i5\frac{12+6i}{5}  

d)

 27+9i5\frac{27+9i}{5}  

4.

 49+73\frac{4}{9+7\sqrt{3}}  Simplify

a)

 −8+7383\frac{-8+7\sqrt{3}}{83}  

b)

 −84+4933\frac{-84+49\sqrt{3}}{3}  

c)

 −18+14333\frac{-18+14\sqrt{3}}{33}  

d)

 −36+323111\frac{-36+32\sqrt{3}}{111}  

5.

 5x4+80x3+315x25x^4+80x^3+315x^2  
FACTOR COMPLETELY.

a)

 5(x+7)(x−9)5\left(x+7\right)\left(x-9\right)  

b)

 5x2(x+7)(x−9)5x^2\left(x+7\right)\left(x-9\right)  

c)

Not factorable.

d)

 5x2(x+7)(x+9)5x^2\left(x+7\right)\left(x+9\right)  

6.

 n3+11n2+28nn^3+11n^2+28n  

FACTOR COMPLETELY.

a)

 n(n+7)(n+4)n\left(n+7\right)\left(n+4\right)  

b)

 n(n+10)n\left(n+10\right)  

c)

 (n+28)(n+1)\left(n+28\right)\left(n+1\right)  

d)

 n(n+2)(n+14)n\left(n+2\right)\left(n+14\right)  

7.

Factor completely.  16a2−24a+916a^2-24a+9  

a)

 (4a+3)(4a−3)\left(4a+3\right)\left(4a-3\right)  

b)

 (−4a−3)(4a−3)\left(-4a-3\right)\left(4a-3\right)  

c)

 (3a−5)2\left(3a-5\right)^2  

d)

 (4a−3)2\left(4a-3\right)^2  

8.

 25x2−125x^2-1  Factor completely.

a)

 (25m+1)2\left(25m+1\right)^2  

b)

 (5m−1)2\left(5m-1\right)^2  

c)

 (5m+1)(5m−1)\left(5m+1\right)\left(5m-1\right)  

d)

 (m+3)(m−3)\left(m+3\right)\left(m-3\right)  

9.

 3k2−8k3k^2-8k  
Factor completely.

a)

 (3k+7)(k+2)\left(3k+7\right)\left(k+2\right)  

b)

 k(3k+8)k\left(3k+8\right)  

c)

 k(3k−8)k\left(3k-8\right)  

d)

 (5k−7)(k−2)\left(5k-7\right)\left(k-2\right)  

10.

 8v2+23v−368v^2+23v-36 
 Factor completely.

a)

 (v−4)(8v+9)\left(v-4\right)\left(8v+9\right)  

b)

 4(2v+1)(v+9)4\left(2v+1\right)\left(v+9\right)  

c)

 2(4v+1)(v−18)2\left(4v+1\right)\left(v-18\right)  

d)

 (v+4)(8v−9)\left(v+4\right)\left(8v-9\right)  

11.

Solve by factoring.

 v2=−1−2vv^2=-1-2v  

a)

 {5,−6}\left\{5,-6\right\}  

b)

 {−1,−7}\left\{-1,-7\right\}  

c)

 {−1,1}\left\{-1,1\right\}  

d)

 {−1}\left\{-1\right\}  

12.

Solve by factoring.

 4n2=−12n+1124n^2=-12n+112 

a)

 {7,8}\left\{7,8\right\}  

b)

 {6,−8}\left\{6,-8\right\}  

c)

 {3,−4}\left\{3,-4\right\}  

d)

 {−7,4}\left\{-7,4\right\}  

13.

Solve by factoring.

 5m2=22m−215m^2=22m-21 

a)

 {85, 3}\left\{\frac{8}{5},\ 3\right\}  

b)

 {45, 4}\left\{\frac{4}{5},\ 4\right\}  

c)

 {75, 3}\left\{\frac{7}{5},\ 3\right\}  

d)

 {−12, 1}\left\{-\frac{1}{2},\ 1\right\}  

14.

Solve by factoring.

 6n2=5n+66n^2=5n+6 

a)

 {32, −23}\left\{\frac{3}{2},\ -\frac{2}{3}\right\}  

b)

 {67, 23}\left\{\frac{6}{7},\ \frac{2}{3}\right\}  

c)

 {−32, 23}\left\{-\frac{3}{2},\ \frac{2}{3}\right\}  

d)

 {−38, 8}\left\{-\frac{3}{8},\ 8\right\}  

15.

Solve by taking square roots. 

 4n2−2=1464n^2-2=146  

a)

 {310, −310}\left\{\frac{3}{10},\ -\frac{3}{10}\right\}  

b)

 {i422, −i422}\left\{\frac{i\sqrt{42}}{2},\ -\frac{i\sqrt{42}}{2}\right\}  

c)

 {37, −37}\left\{\sqrt{37},\ -\sqrt{37}\right\}  

d)

 {i462}\left\{\frac{i\sqrt{46}}{2}\right\}  

16.

 9x2+3=849x^2+3=84  Solve by taking square roots.

a)

 {3,−3}\left\{3,-3\right\}  

b)

 {33,−33}\left\{3\sqrt{3},-3\sqrt{3}\right\}  

c)

 {i1113, −i1113}\left\{\frac{i\sqrt{111}}{3},\ -\frac{i\sqrt{111}}{3}\right\}  

d)

 {74, −74}\left\{\frac{7}{4},\ -\frac{7}{4}\right\}  

17.

Find the value c that completes the square and then rewrite as a perfect square.

 a2+36a+ca^2+36a+c 

a)

 18; (a+18)218;\ \left(a+18\right)^2  

b)

 16; (a−4)216;\ \left(a-4\right)^2  

c)

 121; (a−11)2121;\ \left(a-11\right)^2  

d)

 324; (a+18)2324;\ \left(a+18\right)^2  

18.

Find the value c that completes the square and then rewrite as a perfect square.

 m2+26m+cm^2+26m+c 

a)

 9; (m+3)29;\ \left(m+3\right)^2  

b)

 64; (m+8)264;\ \left(m+8\right)^2  

c)

 676; (m+13)2676;\ \left(m+13\right)^2  

d)

 169; (m+13)2169;\ \left(m+13\right)^2  

19.

Solve by completing the square.

 x2+20x−73=2x^2+20x-73=2  

a)

 {4+67, 4−67}\left\{4+\sqrt{67},\ 4-\sqrt{67}\right\}  

b)

 {−10+57, −10−57}\left\{-10+5\sqrt{7},\ -10-5\sqrt{7}\right\}  

c)

 {24, −4}\left\{24,\ -4\right\}  

d)

 {−8, −12}\left\{-8,\ -12\right\}  

20.

Solve by completing the square.

 x2−8x−23=10x^2-8x-23=10  

a)

 {8+97, 8−97}\left\{8+\sqrt{97},\ 8-\sqrt{97}\right\}  

b)

 {2, −22}\left\{2,\ -22\right\}  

c)

 {11, −3}\left\{11,\ -3\right\}  

d)

 {1+37, 1−37}\left\{1+\sqrt{37},\ 1-\sqrt{37}\right\}  

21.

Solve by completing the square.

 3x2−18x−81=03x^2-18x-81=0  

a)

 {−10+4305, −10−4305}\left\{\frac{-10+4\sqrt{30}}{5},\ \frac{-10-4\sqrt{30}}{5}\right\}  

b)

 {9, −3}\left\{9,\ -3\right\}  

c)

 {1, −3}\left\{1,\ -3\right\}  

d)

 {4, −2}\left\{4,\ -2\right\}  

22.

Solve by completing the square.

 2k2−16k−94=22k^2-16k-94=2  

a)

 {8+47, 8−47}\left\{8+4\sqrt{7},\ 8-4\sqrt{7}\right\}  

b)

 {−4+1384, −4−1384}\left\{\frac{-4+\sqrt{138}}{4},\ \frac{-4-\sqrt{138}}{4}\right\}  

c)

 {3, −1}\left\{3,\ -1\right\}  

d)

 {12, −4}\left\{12,\ -4\right\}  

23.

Find the discriminant then state the number and type of solutions. 

 3a2−2a=73a^2-2a=7  

a)

73; two real solutions

b)

88; two real solutions

c)

-80; two imaginary solutions

d)

-80; one real solution

24.

Find the discriminant then state the number and type of solutions. 

 −v2−6v−14=−5-v^2-6v-14=-5  

a)

0; one real solution

b)

72; two real solutions

c)

0; two imaginary solutions

d)

0; two real solution

25.

Solve using the Quadratic Formula.

 10n2+7=−9n10n^2+7=-9n  

a)

 {i655, −i655}\left\{\frac{i\sqrt{65}}{5},\ -\frac{i\sqrt{65}}{5}\right\}  

b)

 {−9+532, −9−532}\left\{\frac{-9+\sqrt{53}}{2},\ \frac{-9-\sqrt{53}}{2}\right\}  

c)

 {9+i19920, 9−i19920}\left\{\frac{9+i\sqrt{199}}{20},\ \frac{9-i\sqrt{199}}{20}\right\}  

d)

 {655, −655}\left\{\frac{\sqrt{65}}{5},\ -\frac{\sqrt{65}}{5}\right\}  

26.

Solve using the Quadratic Formula.

 10n2=−310n^2=-3  

a)

 {−2+i2, −2−i2}\left\{-2+i\sqrt{2},\ -2-i\sqrt{2}\right\}  

b)

 {−1+i145, −1−145}\left\{\frac{-1+i\sqrt{14}}{5},\ \frac{-1-\sqrt{14}}{5}\right\}  

c)

 {i3010, −i3010}\left\{\frac{i\sqrt{30}}{10},\ -\frac{i\sqrt{30}}{10}\right\}  

d)

 {1+i145, 1−i145}\left\{\frac{1+i\sqrt{14}}{5},\ \frac{1-i\sqrt{14}}{5}\right\}  

27.

 Simplify.

 −8+(−2+6i)−(4i)-8+\left(-2+6i\right)-\left(4i\right) 

a)

 −10−10i-10-10i  

b)

 −6−10i-6-10i  

c)

 −6+2i-6+2i  

d)

 −10+2i-10+2i  

28.

Simplify.

 (1−6i)+(6+7i)\left(1-6i\right)+\left(6+7i\right)  

a)

 −7+i-7+i 

b)

 −5+i-5+i  

c)

 7+13i7+13i  

d)

 7+i7+i  

29.

 (6−7i)(−7−i)\left(6-7i\right)\left(-7-i\right)  

a)

 −42+49i-42+49i  

b)

 35+55i35+55i  

c)

 −35+55i-35+55i  

d)

 −49+43i-49+43i  

30.

 (4+8i)2\left(4+8i\right)^2  

a)

 −48−64i-48-64i  

b)

 −48+64i-48+64i  

c)

 144144  

d)

 196196  

31.

 61+6i\frac{6}{1+6i}  

a)

 6−36i37\frac{6-36i}{37}  

b)

 3−6i5\frac{3-6i}{5}  

c)

 −3−9i10\frac{-3-9i}{10}  

d)

 3−18i37\frac{3-18i}{37}  

32.

 1−5i8+7i\frac{1-5i}{8+7i}  

a)

 −40i−35113\frac{-40i-35}{113}  

b)

 −25−57i149\frac{-25-57i}{149}  

c)

 −27−47i113\frac{-27-47i}{113}  

d)

 1−5i14\frac{1-5i}{14}  

33.

You have a rectangular garden that measures 42 feet by 8 feet. You wan to double the area of the garden by expanding the length and width as shown. Find x.

a)

1212

b)

66

c)

33

d)

22

34.

The height y in feet of a baseball t seconds after it is hit is given by the function
 y=−16t2+96t+3y=-16t^2+96t+3  
Find the maximum height of the ball.

a)

 33  

b)

 6.036.03  

c)

 147147  

d)

 152152  

35.

Use the launched object function.
 −16t2+v0t+h0-16t^2+v_0t+h_0  
A ball thrown to your friend leaves your hand 6 feet above the ground and has an initial velocity of 40 feet per second. How long does it take to reach its maximum height? What is the maximum height of the ball?

a)

 1.251.25 seconds;  3131 feet

b)

 2.552.55 seconds;  31 31\  feet

36.

Use the launched object function.
 −16t2+v0t+h0-16t^2+v_0t+h_0  
A ball thrown to your friend leaves your hand 6 feet above the ground and has an initial velocity of 40 feet per second. Your friend catches the ball when it is 4 feet off the ground. How long is the ball in the air (until your friend catches it)?

a)

 1.551.55 seconds

b)

 2.552.55 seconds

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