Chapter 9
Chapter
R
eview
535
Solving Quadratic Equations Using Square Roots
(pp. 497–502)
9.3
A sprinkler sprays water that covers a cir
cular re
gion of 90
π
square feet. Find the
diameter ofthe circle.
Write an equation using the formula for the area of a circle.
A
π
r
2
Write the formula.
90
π
π
r
2
Substitute
90
π
for
A
.
90
r
2
Divide each side by
π
.
±
√
—
90
r
T
a
ke
the square root of each side.
±
3
√
—
10
r
Simplify
.
A diameter cannot be negati
ve,
so use the positiv
e square root.
The diameter is twice the radius. So, the diameter is 6
√
—
10
.
The diameter of the circle is 6
√
—
10
≈
19 feet.
Solve the equation using square
roots. Round y
our soluti
ons to the nearest hundr
edth,
ifnecessary
.
1
4.
x
2
+
5
17
15.
x
2
14
14
16.
(
x
+
2)
2
64
1
7.
4
x
2
+
25
75
18.
(
x
1)
2
0
19.
19
30
5
x
2
Solving Quadratic Equations by Completing the Square
(pp. 505–514)
9.4
Solve
x
2
−
6
x
4
=
11 by completing the square.
x
2
6
x
+
4
11
Write the equation.
x
2
6
x
7
Subtract 4 from each side
.
x
2
6
x
+
(
3)
2
7
+
(
3)
2
Complete the square by adding
(
6
—
2
)
2
,
or (
3)
2
,
to each side
.
(
x
3)
2
16
W
rite the left side as the square of a binomial.
x
3
±
4
T
a
ke
the square root of each side.
x
3
±
4
Add 3 to each side
.
T
he solutions are
x
3
+
4
7 and
x
3
4
1.
Solve the equation by completing the square
. Round you
r solutions to the nearest hundr
edth,
ifnecessary
.
2
0.
x
2
+
6
x
40
0
21.
x
2
+
2
x
+
5
4
22.
2
x
2
4
x
10
Determine whether the quadratic function has a maximum or minimum v
alue.
Then
nd
thevalue.
2
3.
y
x
2
+
6
x
1
24.
f
(
x
)
x
2
+
4
x
+
11
25.
y
3
x
2
24
x
+
15
2
6.
The width
w
of a credit card is 3 centimeters shorter than the length
ℓ
. The area is
46.75 square centimeters. Find the perimeter
.
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