Podcast
Questions and Answers
What does graphing a quadratic function involve?
What does graphing a quadratic function involve?
What are the types of transformations?
What are the types of transformations?
Translation, vertical stretch and compression, and reflection
The function for translation up is f(x) = (x) + ______
The function for translation up is f(x) = (x) + ______
n
The function for translation down is f(x) = (x) - ______
The function for translation down is f(x) = (x) - ______
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The function for translation left is f(x) = (x + ______)
The function for translation left is f(x) = (x + ______)
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The function for translation right is f(x) = (x - ______)
The function for translation right is f(x) = (x - ______)
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The condition for a vertical stretch is ______ > 1, with f(x) = (______)(x)
The condition for a vertical stretch is ______ > 1, with f(x) = (______)(x)
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A vertical compression occurs at a = 0.
A vertical compression occurs at a = 0.
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Study Notes
Graphing Quadratic Functions
- Involves understanding transformations, standard form, vertex form, and key characteristics of a parabola.
Types of Transformations
- Includes translation (shifting graph), vertical stretch (increasing steepness), vertical compression (decreasing steepness), and reflection (flipping the graph).
Translation Up
- Defined mathematically as f(x) = (x) + n, shifting the graph upward by n units.
Translation Down
- Represented as f(x) = (x) - n, shifting the graph downward by n units.
Translation Left
- Expressed as f(x) = (x + n), which moves the graph left by n units.
Translation Right
- Formulated as f(x) = (x - n), moving the graph right by n units.
Vertical Stretch
- Occurs when a > 1, affecting the steepness of the graph, defined as f(x) = (a > 1)(x).
Vertical Compression
- Happens when 0 < a < 1, reducing the steepness of the graph.
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Description
Test your understanding of graphing quadratic functions, including transformations like translations and vertical stretches. This quiz covers the mathematical definitions and effects of moving parabolas in various directions. Challenge yourself with key characteristics of parabolas and their transformations!
