Name:
Algebra 1
10.3 and 10.4 Part 3 Worksheet
Hour:
Solving Q adratics by Factoring and Taking Square Roots Worksheet
1.
Match each grop.1 A.) its function.
A.
= x2 — I
D. f(x) = 3x2 — 5
B. f(x) = x + 4
C. Px.) = —x2 2 CI
E. f(x) = —3x2 + 8
E Ay) =
+ 5 CI
7;
—1 6
)
b
//' 17a Vela .
h-etiht=
2. A bungee jumper leaves from a platform 256 ft above the ground. Write a quadratic function that gives the jumper's
height h in feet after t secon.s. Then graph the function.
h()
What is the original height of the jumper?
0 )
What will the jumper's height be after 1 second?
li- -160 ) 2.1,256
I)
C
What will the junk rsheight be after 3 seconds?
u -3 )
h
• How far will the jumper have fallen after 3 seconds?
.75-6
-0 A
44
How long before the jumper would hit the ground if she was not attached to a bungee cord?
= L/- Sc(
What values make sense for the domain? What values make sense for the range?
D
DLL
R
How far has the jumper fallen from time t = 0 to t= I?
56
- 2 I/
Does the jumper fall the same distance from time I = 1 to t = 2 as she does
from time t = 0 to t = 1? Show work to support your answer.
----p h
110
NO) Tails 4,4 r
,sces
0.1
Name:
Algebra 1
10.3 and 10.4 Part 4 Worksheet
Hour:
10.3 and 10.4 Word Problems Worksheet
I. Suppose a person is riding in a hot-air balloon, 144 feet above the ground. He drops an apple. The height of the apple
above the ground is given by the formula h = -16t2 +144, where h is height in feet and t is time in seconds.
a. Graph the functio-ri.
b. What is the original height of the apple?
+7=0:
(PI
c. What will the height of the apple be after 4 seconds?
-E=4:
-.1-U4412 4-1LO - llA f4
fDr the L9 1 OWd
d. How far will the apple have fallen after 4 seconds?
144 -Ft
e. How long after the apple is dropped will it hit the ground?
= -/6•62'
hvo:
Mit "I
4
-
Cse c)
f. What values make sense for the domain?
-tfiyi e
g. What values make sense for the range?
A efght
gee.°
h. How far has the apple fallen from time t = 0 to t= 1?
h
0 - I sec
/6
i. Does the apple fall the same distance from time t = 1 to t = 2 as it does from time t = 0 to t = 1?
Show work to support your answer.
iNo
so
g
2. Suppose you have a can of paint that will cover 400 ft2.
Area,
=
70-
a. Find the radius of the largest circle you can paint. Round to the nearest tenth of a foot.
70-.2
qrr
-goo
7r
b. Suppose you have-two cans of paint, which will cover a total of 800 ft2. Find the radius of the largest circle you
can paint. Round to the nearest tenth of a foot.
t/5.95...
-
V
c. Does the radius of the circle double when the amount of paint doubles? Explain.
no,
4-ke, pa 11-16- #9„0,0 con) 40 toaft2 C cReis)
to t d o tth
h tr it
acifu4
otici ho! 11.3
a
-6, /12
3. Suppose a squirrel is in a tree 24 ft above the ground. She drops an acorn.
GrE 2 -V bt
if' Nati "drop° ah °lied/ b
Write a quadratic function for this situation. Then graph the function.
a.
= -/ 6
1-16-6-2 0.14
A
^
= (=
12
v-FT'
s
-L
I,
3
secs .
-b (Se c)
What is a renonable domain and range for the function?
4. Solve each equation by finding square roots.
1 =
O
a. 3d 2 _
12
1- 3cPN = 0 _3
3
1149)*
= iro4 ti) veloci-ty
,
h -1.6et
O
C-
b. 7h2 +0.12 =1.24
7h2 =lJa
7
137-1
a[
2- de
a
A rea
a -1-rleth le
bk
5. Find the value of h for each triangle. If necessary, round to the nearest tenth.
a.
b.
(c2h)( 1-)) •
JO
da
WO
hi° PI
ii
T1—
VT)
ao
a
h
2h
Iliff= ILO t
6.-F
3
6. The sides of a square are all increased y 3 cm. The area of the new square is 64 cm2. Find the length of a side of the
original square.
_X
sbaart
Areit Qç
1
64 X +3)0(4-3)
64 x 2 “X-
64
X+ 11)(X
7. You are building a rectangular wading pool. You want the area of the bottom to be 90 ft2. You want the length of the
pool to be 3 ft longer than twice its width. What will the dimensions of the pool be?
Area_ a ct, recfarui e
go =610,, 3)1.0
go ;2W 230
2.Ki+15 0,
;21,0 2 1-3tAY-990
Gt 4-islau.4
I
b9 6 -ph-
8. The product of two consecutive numbers is 14 less than Yu times the smaller number. Find each number.
x
smaller
bi/ge"
X+I
9. Solve x
2
=
x and x
2
=
(x+-1) /0)(
_ x2 " =it) X
xl -qx4-14
0
(x
—x by factoring. What number is a solution to both equations?
x
X' =
V' • X
X-71
z--
Az, 0,
10. Suppose you throw a baseball into the air with an initial upward velocity of 29 ft/s and an initial height of 6 ft. The
formula h= —16/2 + 29t + 6 gives the ball's height h in feet at time t in seconds.
a. The ball's height h is 0 when it is on the ground.
Find the number of seconds that pass before the ball
lands by solving 0 = —16t2 + 29t +6 .
%
W.
0 17 ---16t2,L3.2-L -3i +4,
b
IIIMIMMFAMEN11111111111111111•1
11•1111111111111•11511111111111111111111111111111111
1111111110111111111111111EMEIMIIIMIll
3C-tO
RA--3)(t 7-a
h
ME111111111=111111WWIREMBIIIIII
111111111B11111111111111MIIIIIIIIMINIII
11111111•1111111111111111M1111111111MMIE
11111M111111111.11111111M1111111111111111111111M
111111111•1111111111111.1111111111111111ffill
t
t
111111111111•111111111111111MMEIMMINIII
INIIIIIIIIIIIMI11111121111111111111111.111M
b. Graph the related function for the equation in art (a)'.
Use your graph to estimate the maximum height of the ball.
AOS • X-.1-
s ci oc256Z-go
111111111111
11111111
111111
- -166 qt)6a5Y4 aqc. 7(tA5)1 1
1111111111111111111MINIIIIIMMOIN
111111111111111MEMMENIIIIIIMIll
MAX
9 ) 19)
11. Suppose the area of the sail shown in the photo is 110 ft2. Find the dimensions of the sail.
Ito
ID
X =3 10
+
2Uf-1
A
(d)(4-d,)
ovc+a
1 ,1°z X 2.4- X
"'= x 2- 4-1( No
12. A square table has an area of 49 ft2. Find the dimensions of the table.
13. Solve the cubic equation: x3 —10x2 + 24x = 0
X(X
.0 /
X
14. You are building a rectangular patio with two rectangular openings for gardens. You have 124 one-foot-square
paving stones. Using the diagram below, what value of x would allow you to use all of the stones?
-ect —
x+-6
A 44('X+0
Areol BC' B.
x2
fr 4-16)(X-0
Area a Skrian
ct =
r
10.3 and 10.4 Part 5 : Word Problems
Read each problem carefully and solve-by factoring or taking square roots.
I. Find the x-intercept(s) and y-intercept(s) of the related function: 2x 2 +6x = 20. Then determine if the graph of the
related function would open up or down.
6x ow
00(
6k -
h
0
4-3)(--
,
5•,x a
2. Set up a quadratic equation and solve it to find the side of a square with an area of 90 ft2. If necessary, round to the
nearest tenth.
qo
3 VT
365
3. A rectangular box has volume 280 in3. Its dimensions are 4 in. x (n + 2) in. x (n + 5) in. Find n.
Use the formula V =
0-11 80 J./ 014 dkh
--- 0 /
/01.
70
_
h
- 70
nl 4 7 h
(0 -1- 1z)(11
\L •
Hour:
Name:
Solving Quadratics by Completing the Square (10.5 Part A)
Solve by completing the square.
ii&et
1. x2 —4x =5
x 2_
c
odd
X 2- 0
=
(x—a)a
=
2. x2 +10x = —21
2
bc1141 sides 24- 10 1-
-Fac-1-Dr
r bah sides
remember
z
X-= 3
) X -;2 -3
4-a 1-:?.
soiv e 2 eq
.
-s-
•--5 -
Solve by completing the square.
3. x2 +6x-91=0
x 2 4-6x
x°1
co
(lit
x2 4-6X-1-
X+3
*10
9
4_11-__)
Solve each equation by completing the square.
5. x2 -12x- 45 = 0
X - 0
7. x2 -2x = 48
8. x2 - 6x-16 = 0,
1177(-7i
c2,5
q9
X 2- 2X -0
A_H---1
X-3'5
X-1
X
-1-3
4-3
114A
10. x2 -16x+28= 0
4491
)( 2 -1t-iX+
A2 —16A
)21
IT O( —7Y—
tri:11
X-7 = -I=It ) )(-7 =-11
X
4-7 +
-----
4-3 413
--c )]
-7-
9. x2 -14x -72 = 0
z
25
P/
17-9-±7
X-1
I
7
2.
X
-
X 1—112/r
R)z
69-
6
Hour:
/3
°
Name:
Solving Quadratics by Completing the Square (10.5 Part B) .
Solve by completing the square.
1. x2 —6x = 0
x2 4--b,k, +
IL'x2 -3x=18 X —
Solve by completing the square.
3. x2 +4x+4=0
-2
=0
Solve each equation by completing the square.
5. x2 —7x = 0
6. x2 +5x= —6
7. x2 —4x=
8. x2 +4x-12 =0
9. x2 +11x+10=0
10. x2 +2x =15
0.41 divide by a ic poicitlee- ,916-1 smeaer
Hour:
Solving Quadratics by Completing the Square (10.5 Part C)
Solve each equation by completing the square.
1. 2x2 +8x =10
2. 2x2 +12x =32
• z
1- 0 =5 ----
*.= /6
6
X 1- 4X -1-14Y1 :: 5
41)(4-q.
?
(7x.T:
2)a ff
x-tI
3. 5x2 +5 =10x.
4. 4x2 -12x = 40
=
/0
9
41-
(351=
A 2 - 3X -1
04 q
4
X5
am-LI
5
6. 3x2 + 6x -9 = 0
3
x
5. 2zJ6x = -30
2X-3
X 4X -15
A d efp--
A2 4- 2)<
X L-1X -1-4
117 x -4) 2 lfl
I
x-- 3 I.
0
3
(
Solve each equation by completing the square.
7. 2x2 -16x+7 = -7
8. 3x2 +30x = -48 .
3
3
—7 —7
A 2 4- ibX 141-1P 16 +,25
A z + 10X
lb
x 2 —X
I
(X f 5)2
9
=
q
±3
X+5
+5
±3
-=
X -L-I_L-73)
n
2(
-7
I
9. Suppose you wish to section off a soccer field as shown in the diagram below. If the area of the field is 450
yd2, find the value of x.
Area
of Rect./kJ-20e
y-1-15
A= baSe x
10
PX-i-JoYx 4,Q0)
e/1(‘2 4- 40/r ADA 4400
#50
X+/5
570
±- 15,11
15,21
-IS -IS-
10
10
X
X
base,- to 4-A
+ to
c2/ " &OA —S O
10
.2
3bX
x
x 2 4_ 30/0.
I,
a
12(
-15go
—/5
ct
gdS" a5-0
tizo
10. A rectangle has a width of x . Its length is 10 feet longer than twice the width. Find the dimensions if its
area is 28 ft2.
,1)( 4-10
A
I
ak-Ft si
x(x+10)::-
2 -
.DR2 /VX 078"
4-
-55X4- (1)2
/V 4
11/-4
5%
(X 4- 35-Y _11 gi
V 4-
x
±1_
n
Hour:
Name:
Solving Quadratics by Using the Quadratic Formula (10.6)
Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth.
g
1. X2 - 4x — 96 =0
3. X2 8x +5 = 0 —
5. x2 —x =132
2. x2 —36 = 0
)
7 3
_II O
rn
9(
6 ) -6
4. 4x2 —12x —91= 0
6. 14x2 =56
0? )
6 .5 -3
Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth.
7. 5x2 =17x+12
8. 4x2 -3x +6 = 0
X 3J
r-g7
x= 17± rag? 4,29-0
.2(5-)
X/7 ±23
/0
ID
3
10
9. x2 -6x = -9
10. 2x2 +6x-8=0
x2.---6X+9
-3±
11. A rectangular painting has dimensions x and x + 10. The painting is in a frame 2 in. wide. The total area of
the picture and the frame is 144 in2. What are the dimensions of the painting? I
(A/4-1q)(X-4-1/) 't4ct
2+1(14o4-2
to
2
1
-- xi- 14
12. A ball is thrown upward from the top of a building at a height of 44 ft with an initial upward velocity
of 10 ft/s. Use the formula h = -16t2 + vt + s to find out how long it will take for the ball to hit the ground.
-05