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Chapter 4 -
Quadratic Functions
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The Vertex Form - Transformations and
Graphing Techniques |
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Team members |
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Name: Tutu Udoh-Orok
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Overview |
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{Describe what this
section is about. Outline the major concepts.
What should students expect in terms of standard
type of question?.}
This section focuses on
identifying types of transformations and
graphing techniques for quadratic functions.
Vertex Form
y = a(x+p)
vertex ( -p , q )
Using the p value the
following can be identified:
- Axis of symmetry
- Horizontal shift
- If p>0, shift left
- If p<0, shift
right
Using the q value, the
following can be identified:
- Maximum/Minimum value
- Range
- Vertical Displacement
Using the a value, the
vertical change can be identified:
- 0<a< 1 vertical
compression
- a>1 vertical stretch
Using the a value again,
it can also be determined if theres a
reflection in the x-axis
- a>0 minimum (positive
value. No reflection in x-axis. Opens Up)
- a<0 maximum (negative
value. Reflection in x-axis. Opens Down)
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Study Tips,
Methods and or Advice |
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{Give useful study tips.
Describe any useful methods or techniques used
to solve standard type of questions}
1.
When graphing, find major
key points (Vertex, x-intercept(s), y-intercept)
2.
Remember factoring and
quadratic equation when finding the x-intercept(s)
3.
Understand all the
italicized terms in the questions : (Factoring,
x intercepts, y intercepts, completing the
square, vertex and vertex form, axis of
symmetry, direction of opening, maximum and
minimum values)
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Sample
Questions and complete solutions |
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{ Provide 3 to 4
standard type of question with complete
solution}
Graph the following
functions and label key points. For the first 2
questions, solve for the x intercept using the
factoring method. For the last 2 questions,
solve for x using the quadratic equation. If
necessary, round all answers to 4 decimal
places.
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Questions |
Complete Solutions |
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1. y = x
4x - 21
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Factoring
y = x
4x - 21
= x-
7x + 3x 21
= x (x - 7) + 3(x - 7)
= (x - 7)(x + 3)
x intercepts
(7,0) (-3,0)
y intercept
(0, -21)
Completing the
square
 = 4
y = x
4x - 21
= (x-
4x) 21
= (x -
4x + 4 4) -21
= (x 2)-25
Vertex (2,
-25)
Axis of symmetry
x = 2
Direction of
opening: Up
Maximum/Minimum
Value: Minimum
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2.
y = -3x
18x + 48
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y = -3x
18x + 48
= -3(x+
6x 16)
= -3(x+
8x -2x - 16)
= -3(x (x + 8) - 2(x + 8))
= -3(x + 8)(x
2)
x intercepts
(-8,0) (2,0)
y intercept
(0, 48)
Completing the
square
= 9
y = x
18x + 48
= -3(x+
6x) + 48
= -3(x +
6x + 9 - 9) + 48
= -3(x+
6x + 9)+
27 + 48
= -3(x + 3)
+
75
Vertex (-3,
75)
Axis of symmetry
x = -3
Direction of
opening: Down
Maximum/Minimum
Value: Maximum
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3.
y = x
2x -35
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Quadratic
Equation
y = x
2x -35
x intercepts
(7,0) (-5,0)
y intercept
(0, -35)
Completing the
square
= 1
y = x
2x - 35
= (x+
2x + 1 1) 35
= (x +
2x +1) 1 35
= (x 1)
36
Vertex
(1, 36)
Axis of symmetry
x = 1
Direction of
opening: Up
Maximum/Minimum
Value: Minimum
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4.
y = 8x +
6x -9
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Quadratic
Equation
y = 8x +
6x -9
x intercepts
(,0)
(,0)
y intercept
(-9, 0)
Completing the
square
= 9
y = 8x +
6x -9
= 8(x+
6x + 9 - 9) 9
= 8(x +
6x +1) 9 72
= 8(x + 3)
81
Vertex (3,
81)
Axis of symmetry
x = 3
Direction of
opening: Up
Maximum/Minimum
Value: Minimum
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Extra
Practice Questions and Answers |
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{Provide 5 extra
practice questions with answers only}
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Extra Practice Questions |
Answers |
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1.
y = x -
10x + 11
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x intercepts (8.7417,
0) (1.2583, 0)
y intercept (0, 11)
Vertex (5,
14)
Axis of symmetry
x = 5
Direction of
opening: Up
Maximum/Minimum
Value: Minimum |
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2.
y = 2x +
8x + 7
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x intercepts (1.2929,
0) (2.7071, 0)
y intercept (0, 7)
Vertex (2,
1)
Axis of symmetry
x = 2
Direction of
opening: Up
Maximum/Minimum
Value: Minimum |
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3. y = -x +
4x + 5
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x intercepts (5,
0) (1, 0)
y intercept (0, 5)
Vertex (2, 9)
Axis of symmetry
x = 2
Direction of
opening: Down
Maximum/Minimum
Value: Maximum |
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4. y = 2x -
6x -20
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x intercepts (5, 0) (2,
0)
y intercept (0,
20)
Vertex (1.5,
24.5)
Axis of symmetry
x = 1.5
Direction of
opening: Up
Maximum/Minimum
Value: Minimum |
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5.
y = 4x +
22x + 5
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x intercepts (0.2375,
0) (5.2625, 0)
y intercept (0,
5)
Vertex (2.75,
25.25)
Axis of symmetry
x = 2.75
Direction of
opening: Up
Maximum/Minimum
Value: Minimum |
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Self
Reflection |
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{Each student
individually states in a paragraph or two a
personal reflection about this topic. State
what you like or didnt like about this topic.
What was interesting or challenging or important
to know about this topic? Give any useful
feedback either about the topic, course and/or
design of your web page.}
Personal Reflection -
Nektaria
Personal Reflection -
????????
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