p.132-135

chapter
two
Equations and Inequalities of One Variable
ho = 50 ft
Vo
= 60
ft/s
50 ft
o = -16t2 + 60t +' 50
The
0= 8t2 - 30t ~ 25
good method
t
30 ± ..}900 + 800
= ---16
30 ± 1O.Ji7
t=--16
quadratic
polynomial
in the equation
factor over the integers. so the quadratic
is a
to use. To simplify the calculations,
we
can begin by dividing both sides of the equation
by
-2.
We then proceed to reduce the radical and simplify
the resulting fraction (which actuaHy describes two
solutions ).
15 ± 5.Ji7
t=---
These numbers
t",,~,4.45
The negative solution is immaterial in this problem, as
this represents a time before the ball is thrown, so it
8
is discarded.
thrown.
are most meaningful
3x2
4x2+
-7x
-339 =2X2
=
0 +18
9x-5x2
-3x=
=-2x2
+ 14x
1. 2X2
2x2-x=3
132
in decimal form.
The ball lands 4.45 seconds
Solve the following quadratic equations by factoring. See Example 1.
3.
9.
5x2
3 = 4x2 + 6x -1
5.
y(2y+
9)+=-9
7. x2-14x+49=0
(3x+2)(x-l)=7-7x
11.+ 2x
(x-7)2=16
doesn't
formula
6.
2.
4. 15x2 +x = 2
..10.
12.
8.
after being
section
2.3
Quadratic Equations in One Variable
x2-6x+9=-16
2X2
u2+10u+9=0
+6x-10
10 33.
Z2+26z+2
= =-23
21.
x2-4x+4=49
27.
29.
2x2+7x-1S=0
32.
26.
30.
4x2
-56x++9=0
195
0
14.
(a-2(=-S
-1=0
23.
17.
(3x-6)2
=4x2
y2+22y+96=0
Solve (Y_18)2
the following-quadratic
equations
the= square
root method. See Example 2.
15. 20.
0by
24.
(2x+3)2
18.
9(8t-3)2
= (3s+ ~2)2
0
25. See
x2 +Example
8x += 79 = -8
13.
(X_3)2
dratic
equations by completing the square.
3.
Solve the follow~ng quadratic equations by using the quadratic formula. See Example 4.
2X2
3x2
+8x-3
6x==-1
6x0=- 30 50.
3x2-4=-x
7x2
3a2
-42x
+--5x-lO:;=
-4x
12a-576
0=lOz
4Z2
14z
==
38.
57.
44.
56.
34. 7x2
y2
l+24y+23=0
4x2
-2y+1
-3x
=-1
-289
53.
42.
51.
41.
4x2-14x-27=3
x2
==27
47.
59.
39.
3x2
0 -768
5x2
·(z-11)2
a(a+
(y_8)2
2)
===
36
9051
45. 35.
x2 -6x
+-2x
20x+36
=-48
36.
2.1l-3.Sy=4
54.
-3(b+
5)2
48.
(9Y_6)2
= =121y2
Solve the following quadratic equations using any appropriate method.
20 60. 4w2 + 10w+5 = 3w2 + 18w-1O 43. l +9y = -40.50
/
133
chapter two
Equations and Inequalities of One Variable
Solve the following application problems. See Example 5.
61. How long would it take for a ball dropped from the top of a 144-foot building to
hit the ground?
62. Suppose that instead of being dropped, as in problem 61, a ball is thrown upward
with a velocity of 40 feet per second from the top of a 144-foot building. Assuming
it misses the building on the way back down, how long after being thrown will it
hit the ground?
= 144 ft
Vo = 40 ft/sec
ho
144 ft
63. A slingshot is used to shoot a BB at a velocity of 96 feet per second straight up
from ground level. When will the BB r~ach its maximum height of 144 feet?
64. A rock is thrown upward with a velocity of 20 meters per second from the top
of a 24 meter high cliff, and it misses the cliff on the way back down. When
will the rock be 7 -meters from ground level? (Round your answer to the
nearest tenth.)
134
section2~3 .
Quadratic Equations in One Variable
65. Luke, an experienced bungee jumper, leaps from· a tall bridge and falls toward
the river below. The bridge is 170 feet above the water and Luke's bungee cord is
110 feet long unstretched. When will Luke's cord begin to stretch? (Round your
answer to the nearest tenth.)
Use the connection between solutions of quadratic equations and polynomial factoring to
answer the following questions. See the discussion after Example 3.
66. Factor the quadratic
x2
67. Factor thy quadratic 9x2
6x + 13.
-
-
6x - 4.
68. Factor the quadratic 4x2 + 12x + 1.
69. Factor the quadratic 25x2 -lOx + 2.
70. Determine
band
c so that the equation
x2
+ bx + c = 0 has the solution set
{-3,8}.
135