9-1 Quadratic Equations and Functions

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Lesson Quizzes
Preview
9-1 Quadratic Equations and Functions 9-2
Characteristics of Quadratic Functions 9-3
Graphing Quadratic Functions 9-4 Solving
Quadratic Equations by Graphing 9-5 Solving
Quadratic Equations by Factoring 9-6 Solving
Quadratic Equations by Using Square Roots 9-7
Completing the Square 9-8 The Quadratic
Formula 9-9 The Discriminant
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9-1 Quadratic Equations and Functions
Lesson Quiz Part I
1. Without graphing, tell whether (3, 12) is on
the graph of y 2x2 5. 2. Graph y 1.5x2.

no
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9-1 Quadratic Equations and Functions
Lesson Quiz Part II
Use the graph for Problems 3-5. 3. Identify the
vertex. 4. Does the function have a minimum
or maximum? What is it? 5. Find the domain and
range.
(5, 4)
maximum 4
D all real numbers R y 4
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9-2 Characteristics of Quadratic Functions
Lesson Quiz Part I

• 1. Find the zeros and the axis of symmetry.
• 2. Find the axis of symmetry and the vertex of
  the graph of y 3x2 12x 8.

zeros 6, 2 x 2
x 2 (2, 4)
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9-2 Characteristics of Quadratic Functions
Lesson Quiz Part II
3. The graph of f(x) 0.01x2 x can be used to
model the height in feet of a curved arch support
for a bridge, where the x-axis represents the
water level and x represents the distance in feet
from where the arch support enters the water.
Find the height of the highest point of the
bridge.

25 feet
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9-3 Graphing Quadratic Functions
Lesson Quiz
1. Graph y 2x2 8x 4.
2. The height in feet of a fireworks shell can be
modeled by h(t) 16t2 224t, where t is the
time in seconds after it is fired. Find the
maximum height of the shell, the time it takes to
reach its maximum height, and length of time the
shell is in the air.
784 ft 7 s 14 s
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9-4 Solving Quadratic Equations by Graphing
Lesson Quiz
Solve each equation by graphing the related
function. 1. 3x2 12 0 2. x2 2x 8 3. 3x
5 x2 4. 3x2 3 6x 5. A rocket is shot
straight up from the ground. The quadratic
function f(t) 16t2 96t models the rockets
height above the ground after t seconds. How
long does it take for the rocket to return to
the ground?
2, 2
4, 2
ø
1
6 s
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9-5 Solving Quadratic Equations by Factoring
Lesson Quiz Part I
Use the Zero Product Property to solve each
equation. Check your answers. 1. (x 10)(x 5)
0 2. (x 5)(x) 0 Solve each quadratic
equation by factoring. Check your answer. 3. x2
16x 48 0 4. x2 11x 24
10, 5
5, 0
4, 12
3, 8
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9-5 Solving Quadratic Equations by Factoring
Lesson Quiz Part II
1, 7
5. 2x2 12x 14 0
9
6. x2 18x 81 0
2
7. 4x2 16x 16
8. The height of a rocket launched upward from a
160 foot cliff is modeled by the function h(t)
16t2 48t 160, where h is height in feet and
t is time in seconds. Find the time it takes the
rocket to reach the ground at the bottom of the
cliff.
5 s
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9-6 Solving Quadratic Equations by Using Square
Roots
Lesson Quiz Part I
Solve using square roots. Check your answers. 1.
x2 195 1 2. 4x2 18 9 3. 2x2 10 12
4. Solve 0 5x2 225. Round to the nearest
hundredth.
14
ø
6.71
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9-6 Solving Quadratic Equations by Using Square
Roots
Lesson Quiz Part II
5. A community swimming pool is in the shape of a
trapezoid. The height of the trapezoid is twice
as long as the shorter base and the longer base
is twice as long as the height.
The area of the pool is 3675 square feet. What is
the length of the longer base? Round to the
nearest foot.
108 feet
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9-7 Completing the Square
Lesson Quiz Part I
Complete the square to form a perfect square
trinomial. 1. x2 11x 2. x2 18x Solve
by completing the square. 3. x2 2x 1 0 4.
3x2 6x 144 5. 4x2 44x 23
81
6, 8
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9-7 Completing the Square
Lesson Quiz Part II
6. Dymond is painting a rectangular banner for a
football game. She has enough paint to cover 120
ft2. She wants the length of the banner to be 7
ft longer than the width. What dimensions should
Dymond use for the banner?
8 feet by 15 feet
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9-8 The Quadratic Formula
Lesson Quiz
1. Solve x2 x 12 by using the Quadratic
Formula. 2. Solve 3x2 5x 1 by using the
Quadratic Formula. 3. Solve 8x2 13x 6 0.
Use at least 2 different methods.
3, 4
0.23, 1.43
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9-9 The Discriminant
Lesson Quiz
1. Find the number of solutions of 5x2 19x 8
0 by using the discriminant. 2. Find the
number of x-intercepts of y 3x2 2x 4 by
using the discriminant. 3. An object is shot
up from 4 ft off the ground with an initial
velocity of 48 ft/s. Will it reach a height of 40
ft? Use the discriminant to explain your answer.
2
2
The discriminant is 0. The object will reach its
maximum height of 40 ft once.