Section 9.4
S
olving Quadrati
c Equations by Comple
ting the Square
511
Exerci
ses
9.4
Dynamic Solutions
available at
BigIdeasMath.c
om
In Exer
cises 5–10,
nd the value of
c
that completes
thesquare.
5.
x
2
8
x
+
c
6.
x
2
2
x
+
c
7.
x
2
+
4
x
+
c
8.
x
2
+
12
x
+
c
9.
x
2
15
x
+
c
10.
x
2
+
9
x
+
c
In Exercises 11–16, complete the squar
e fo
r the
expr
ession.
Then factor the trinomial.
(
See Example 1.)
11.
x
2
10
x
12.
x
2
40
x
13.
x
2
+
16
x
14.
x
2
+
22
x
15.
x
2
+
5
x
16.
x
2
3
x
In Exercises 17–22, solv
e the equation by completing the
square. Round y
our solutio
ns to the nearest hundr
edth,
if necessary
.
(
See Example 2.)
17.
x
2
+
14
x
15
18.
x
2
6
x
16
19.
x
2
4
x
2
20.
x
2
+
2
x
5
21.
x
2
5
x
8
22.
x
2
+
11
x
10
23.
MODELING WITH
MA
THEMA
TICS
The area of the
patio is 216 square feet.
a.
Write an equation
that represents the
area of the patio.
b.
Find the dimensions of
the patio by completing
the square.
24.
MODELING WITH
MA
THEMA
TICS
Some sand art
contains sand and water sealed in a glass case, similar
to the one sho
wn.
When the art is turned upside do
wn,
the sand and water fall to create a ne
w pict
ure. The
glass case has a depth of 1 centimeter and a volume
of768 cubic centimeters.
x
x
cm
cm
(
x
2
8) cm
a.
Write an equation that represents the volume of
the glass case.
b.
Find the dimensions of the glass case by
completing the square.
In Exercises 25–
32, s
olve the equation by completing the
square. Round y
our solutio
ns to the nearest hundr
edth,
if necessary
.
(
See Example 3.)
25.
x
2
8
x
+
15
0
26.
x
2
+
4
x
21
0
27
.
2
x
2
+
20
x
+
44
0
28.
3
x
2
18
x
+
12
0
29.
3
x
2
24
x
+
17
40
30.
5
x
2
20
x
+
35
30
31.
2
x
2
14
x
+
10
26
32.
4
x
2
+
12
x
15
5
Monitoring P
rogres
s and Modeling
with Mathematic
s
Monitoring Progr
ess and
Modeling with Mathematics
1.
COMPLETE THE S
ENTENCE
The process of adding a constant
c
to the expression
x
2
+
bx
so that
x
2
+
bx
+
c
is a perfect square trinomial is called ________________.
2.
VOCABULARY
Explain how
to complete the square for an expression of the form
x
2
+
bx
.
3.
WRITING
Is it more conv
enient to complete the square for
x
2
+
bx
when
b
is odd or when
b
is ev
en?
Explain.
4.
WRITING
Describe ho
w you can use the process of completing the square to
nd the maximum or
minimum va
lue of a quadratic function.
Voca
bulary
and Core
Concept Check
Voca
bulary
and Core Concept
Check
x
ft
(
x
+
6) ft
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