Quadratic Equation Worksheet - Completing The Square Page 5

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G
P
UIDED
RACTICE
Vocabulary Check
Describe what it means to “complete the square” for an expression of the form
1.
2
x
+ bx.
Concept Check
Which method for solving quadratic
2.
equations—factoring or completing the
2
y = ºx
º 6x + 4
square—is more general? Explain.
2
+ 6x) + 4
y = º(x
2
y + 9 = º(x
+ 6x + 9) + 4
E
A
A student tried to write
3.
RROR
NALYSIS
2
2
y + 9 = º(x + 3)
+ 4
y = ºx
º 6x + 4 in vertex form as shown.
2
Explain the student’s mistake. Then write the
y = º(x + 3)
º 5
correct vertex form of the function.
Skill Check
Find the value of c that makes the expression a perfect square trinomial. Then
write the expression as the square of a binomial.
2
2
2
x
+ 2x + c
x
+ 14x + c
x
º 6x + c
4.
5.
6.
2
2
2
7.
x
º 10x + c
8.
x
+ 5x + c
9.
x
º 13x + c
Solve the equation by completing the square.
2
2
2
10.
x
+ 4x = º1
11.
x
º 2x = 4
12.
x
º 16x + 76 = 0
2
2
2
x
+ 8x + 9 = 0
2x
+ 12x = 4
3x
º 12x + 93 = 0
13.
14.
15.
Write the quadratic function in vertex form and identify the vertex.
2
2
2
16.
y = x
+ 12x
17.
y = x
º 4x + 7
18.
y = x
º 8x + 31
2
2
2
y = x
+ 10x + 17
y = ºx
+ 14x º 45
y = 2x
+ 4x º 4
19.
20.
21.
22.
L
D
Suppose the homeowner in Example 5 has 60 feet
ANDSCAPE
ESIGN
of wire mesh to put around the garden and enough mulch to cover an area of
140 square feet. What should the dimensions of the garden be?
P
A
RACTICE
PPLICATIONS
AND
R
E
Write the expression as the square of a binomial.
EWRITING
XPRESSIONS
S
H
TUDENT
ELP
2
2
2
Extra Practice
x
+ 16x + 64
x
+ 20x + 100
x
º 24x + 144
23.
24.
25.
to help you master
2
2
2
26.
x
º 38x + 361
27.
x
+ x + 0.25
28.
x
º 1.4x + 0.49
skills is on p. 946.
9
1
1
4
4
2
2
2
29.
x
º 3x +
30.
x
+
x +
31.
x
º
x +
4
6
1
44
9
8
1
C
S
Find the value of c that makes the expression a
OMPLETING THE
QUARE
perfect square trinomial. Then write the expression as the square of a binomial.
2
2
2
x
º 12x + c
x
+ 18x + c
x
+ 26x + c
32.
33.
34.
2
2
2
35.
x
º 44x + c
36.
x
+ 9x + c
37.
x
º 11x + c
2
2
2
x
º 23x + c
x
+ 15x + c
x
º 0.2x + c
38.
39.
40.
2
2
2
41.
x
º 5.8x + c
42.
x
+ 1.6x + c
43.
x
+ 9.4x + c
2
1
0
1
7
2
2
2
44.
x
º
x + c
45.
x
+
x + c
46.
x
+
x + c
7
3
8
286
Chapter 5 Quadratic Functions

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