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Questions and Answers
What is the vertex of the quadratic relation $y = -(x-2)^2 + 9$?
What is the vertex of the quadratic relation $y = -(x-2)^2 + 9$?
- (-2, 9)
- (2, -9)
- (2, 9) (correct)
- (9, 2)
The quadratic function $y = 2(x + 7)^2 - 4$ opens downwards.
The quadratic function $y = 2(x + 7)^2 - 4$ opens downwards.
False (B)
What is the axis of symmetry for the function $y = -(x-2)^2 + 9$?
What is the axis of symmetry for the function $y = -(x-2)^2 + 9$?
x = 2
The function $y = 2(x + 7)^2 - 4$ has its vertex at the point (______, ______).
The function $y = 2(x + 7)^2 - 4$ has its vertex at the point (______, ______).
Match the transformation with its description:
Match the transformation with its description:
Which transformation describes $y = -(x - 2)^2 + 9$?
Which transformation describes $y = -(x - 2)^2 + 9$?
Identify the direction of opening for the quadratic relation $y = 2(x + 7)^2 - 4$. What is it?
Identify the direction of opening for the quadratic relation $y = 2(x + 7)^2 - 4$. What is it?
The step pattern for the quadratic function $y = -(x-2)^2 + 9$ is __________.
The step pattern for the quadratic function $y = -(x-2)^2 + 9$ is __________.
What is the expression of the quadratic relation derived from the transformations provided?
What is the expression of the quadratic relation derived from the transformations provided?
The expression y = 6(2x^2 - 2) represents a quadratic equation.
The expression y = 6(2x^2 - 2) represents a quadratic equation.
What is the vertex form of a quadratic equation?
What is the vertex form of a quadratic equation?
The ______ transformation involves shifting the graph of the function vertically.
The ______ transformation involves shifting the graph of the function vertically.
Match the following parts of a quadratic relation with their descriptions:
Match the following parts of a quadratic relation with their descriptions:
What is the vertex of the quadratic relation given by the equation $y = 2(x - 1)^2 + 3$?
What is the vertex of the quadratic relation given by the equation $y = 2(x - 1)^2 + 3$?
A quadratic relation can be written in vertex form, standard form, and factored form.
A quadratic relation can be written in vertex form, standard form, and factored form.
In the equation $y = 2(x - 1)^2 + 3$, what is the value of 'a'?
In the equation $y = 2(x - 1)^2 + 3$, what is the value of 'a'?
The quadratic relation $y = 3(x + 1)^2 - 2$ can be rewritten in standard form as $y = _____$.
The quadratic relation $y = 3(x + 1)^2 - 2$ can be rewritten in standard form as $y = _____$.
Match each term to its description:
Match each term to its description:
Flashcards
Completing the Square
Completing the Square
In a quadratic expression, Completing the Square is a technique used to transform the expression into a perfect square trinomial, which enables you to rewrite the expression in vertex form.
Vertex Form of a Quadratic Relation
Vertex Form of a Quadratic Relation
The vertex form of a quadratic relation is given by y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Perfect Square Trinomial
Perfect Square Trinomial
A perfect square trinomial is a trinomial that can be factored as the square of a binomial. For example, x^2 + 6x + 9 is a perfect square trinomial because it can be factored as (x + 3)^2.
Standard Form of a Quadratic Relation
Standard Form of a Quadratic Relation
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Changing Forms of Quadratic Equations
Changing Forms of Quadratic Equations
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Vertex
Vertex
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Axis of Symmetry
Axis of Symmetry
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Direction of Opening
Direction of Opening
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Maximum/Minimum Value
Maximum/Minimum Value
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Vertical Stretch/Compression
Vertical Stretch/Compression
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Horizontal Shift
Horizontal Shift
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Vertical Shift
Vertical Shift
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Vertical Reflection
Vertical Reflection
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Vertex Form of a Quadratic
Vertex Form of a Quadratic
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Vertical Stretch/Compression Factor
Vertical Stretch/Compression Factor
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Study Notes
Unit 3 - Vertex Form Test Re-Write
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Quadratic Transformations (a):
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Relation: y = (x - 2)² + 9
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Vertex: (2, 9)
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Axis of Symmetry: x = 2
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Maximum Value: 9
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Step Pattern: 1, 3, 5
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Transformations: Horizontal shift 2 units right, vertical shift 9 units up
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Quadratic Transformations (b):
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Relation: y = 2(x + 7)² – 4
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Vertex: (-7, -4)
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Axis of Symmetry: x = -7
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Minimum Value: -4
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Step Pattern: 2, 6, 10
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Transformations: Vertical stretch by a factor of 2, horizontal shift 7 units left, vertical shift 4 units down
Completing the Square
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Example (a):
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Relation: y = 2x² - 4x + 5
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Vertex form: y = 2(x - 1)² + 3
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Vertex: (1, 3)
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Example (b):
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Relation(a) :y = 3(x + 1)² – 2 Standard form: y = 3x² + 6x + 4
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Relation(b) :y = 2(x + 1)(2x – 2) Standard form: y = 4x² - 4
Spicy Vertex Form
- Transformations:
- Vertical reflection across the x-axis
- Vertical stretch by a factor of 4
- Horizontal shift 5 units to the right
- Vertical shift 2 units up
- Quadratic relation: y = -4(x - 5)² + 2
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Description
This quiz focuses on understanding quadratic transformations and the process of completing the square. It covers concepts such as vertex form, axis of symmetry, maximum and minimum values, and various transformations. Test your knowledge on how to rewrite quadratic equations in vertex form and identify their characteristics.
