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Lesson Quizzes
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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
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. no
2. Graph y = 1.5x2.
9-1 Quadratic Equations and Functions
Lesson Quiz: Part II
Use the graph for Problems 3-5.
3. Identify the vertex.
(5, –4)
4. Does the function have a
minimum or maximum? What is
it? maximum; –4
5. Find the domain and range.
D: all real numbers;
R: y ≤ –4
9-2 Characteristics of Quadratic Functions
Lesson Quiz: Part I
1. Find the zeros and the axis of symmetry.
zeros: –6, 2; x = –2
2. Find the axis of symmetry and the vertex of the
graph of y = 3x2 + 12x + 8.
x = –2; (–2, –4)
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
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
9-4 Solving Quadratic Equations by Graphing
Lesson Quiz
Solve each equation by graphing the related
function.
1. 3x2 – 12 = 0 2, –2
2. x2 + 2x = 8 –4, 2
3. 3x – 5 = x2
ø
4. 3x2 + 3 = 6x 1
5. A rocket is shot straight up from the ground.
The quadratic function f(t) = –16t2 + 96t
models the rocket’s height above the ground
after t seconds. How long does it take for the
rocket to return to the ground? 6 s
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 10, –5
2. (x + 5)(x) = 0
–5, 0
Solve each quadratic equation by factoring.
Check your answer.
3. x2 + 16x + 48 = 0 –4, –12
4. x2 – 11x = –24 3, 8
9-5 Solving Quadratic Equations by Factoring
Lesson Quiz: Part II
5. 2x2 + 12x – 14 = 0 1, –7
6. x2 + 18x + 81 = 0
7. –4x2 = 16x + 16
–9
–2
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.
5s
9-6 Solving Quadratic Equations by Using Square Roots
Lesson Quiz: Part I
Solve using square roots. Check your answers.
1. x2 – 195 = 1
± 14
2. 4x2 – 18 = –9
3. 2x2 – 10 = –12 ø
4. Solve 0 = –5x2 + 225. Round to the nearest
hundredth. ± 6.71
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.
(Hint: Use
108 feet
)
9-7 Completing the Square
Lesson Quiz: Part I
Complete the square to form a perfect square
trinomial.
1. x2 + 11x +
2. x2 – 18x +
81
Solve by completing the square.
3. x2 – 2x – 1 = 0
4. 3x2 + 6x = 144
5. 4x2 + 44x = 23
6, –8
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
9-8 The Quadratic Formula
Lesson Quiz
1. Solve x2 + x = 12 by using the Quadratic Formula.
3, –4
2. Solve –3x2 + 5x = 1 by using the Quadratic
Formula. = 0.23, ≈ 1.43
3. Solve 8x2 – 13x – 6 = 0. Use at least 2 different
methods.
9-9 The Discriminant
Lesson Quiz
1. Find the number of solutions of 5x2 – 19x – 8 = 0
by using the discriminant. 2
2. Find the number of x-intercepts of
y = –3x2 + 2x – 4 by using the discriminant. 2
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.
The discriminant is 0. The object will reach its
maximum height of 40 ft once.