Chapter 5 Quadratic Functions - 5.6 The Quadratic Formula And The Discriminant Worksheet Template Page 5
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G
P
UIDED
RACTICE
2
Vocabulary Check
In the quadratic formula, what is the expression b
º 4ac called?
1.
Concept Check
2.
How many solutions does a quadratic equation have if its discriminant
is positive? if its discriminant is zero? if its discriminant is negative?
Describe a real-life situation in which you can use the model
3.
2
2
h = º16t
+ v
t + h
but not the model h = º16t
+ h
.
0
0
0
Skill Check
Use the quadratic formula to solve the equation.
2
2
4.
x
º 4x + 3 = 0
5.
x
+ x º 1 = 0
2
2
2x
+ 3x + 5 = 0
9x
+ 6x º 1 = 0
6.
7.
2
2
2
8.
ºx
+ 8x = 1
9.
5x
º 2x + 37 = x
+ 2x
Find the discriminant of the quadratic equation and give the number and type
of solutions of the equation.
2
2
2
x
+ 5x + 2 = 0
x
+ 2x + 5 = 0
4x
º 4x + 1 = 0
10.
11.
12.
2
2
2
13.
º2x
+ 3x º 7 = 0
14.
9x
+ 12x + 4 = 0
15.
5x
º x º 13 = 0
B
A basketball player passes the ball to a teammate who
16.
ASKETBALL
catches it 11 ft above the court, just above the rim of the basket, and slam-dunks
it through the hoop. (This play is called an “alley-oop.”) The first player releases
the ball 5 ft above the court with an initial vertical velocity of 21 ft/sec. How
long is the ball in the air before being caught, assuming it is caught as it rises?
P
A
RACTICE
PPLICATIONS
AND
E
S
F
Use the quadratic formula to solve
QUATIONS IN
TANDARD
ORM
S
H
TUDENT
ELP
the equation.
Extra Practice
2
2
2
to help you master
x
º 5x º 14 = 0
x
+ 3x º 2 = 0
x
º 2x º 4 = 0
17.
18.
19.
skills is on p. 946.
2
2
2
20.
x
+ 10x + 22 = 0
21.
x
+ 6x + 58 = 0
22.
ºx
+ 7x º 19 = 0
2
2
2
5x
+ 3x º 1 = 0
3x
º 11x º 4 = 0
2x
+ x + 1 = 0
23.
24.
25.
2
2
2
26.
6p
º 8p + 3 = 0
27.
º7q
+ 2q + 9 = 0
28.
8r
+ 4r + 5 = 0
2
2
2
º4t
º 9t º 3 = 0
9u
º 12u + 85 = 0
10v
+ 8v º 1 = 0
29.
30.
31.
E
S
F
Use the quadratic formula to solve
QUATIONS NOT IN
TANDARD
ORM
the equation.
2
2
x
+ 4x = º20
x
º 2x = 99
32.
33.
2
2
34.
x
+ 14 = 10x
35.
x
= 8x º 35
2
2
ºx
º 3x = º7
ºx
= 16x + 46
36.
37.
S
H
TUDENT
ELP
2
2
3x
+ 6x = º2
8x
º 8x = 1
38.
39.
HOMEWORK HELP
2
2
2
2
40.
5x
+ 9x = ºx
+ 5x + 1
41.
40x º 7x
= 101 º 3x
Examples 1–3: Exs. 17–55
Example 4: Exs. 56–64
2
2
2
2
º16k
= 20k
+ 24k + 5
13n
+ 11n º 9 = 4n
º n º 4
42.
43.
Example 5: Exs. 74–80
2
2
2
44.
3(d º 1)
= 4d + 2
45.
3.5y
+ 2.6y º 8.2 = º0.4y
º 6.9y
5.6 The Quadratic Formula and the Discriminant
295
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