Questions and Answers
What is the name for all transformations that do not change the shape of the graph?
Rigid transformation
If a parabola is in standard position, what is the vertex?
(0,0)
What is the parent function of a parabola in standard position?
f(x) = x^2
What type of transformation is represented by f(x) = x^2 + 4?
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What type of transformation is represented by f(x) = (x + 1)^2?
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What type of transformation is represented by F(x) = 12x^2?
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What type of transformation is represented by F(x) = -x^2?
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What type of transformation is represented by F(x) = 1/5x^2?
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Determine the values of F(x) = x^2 - 3 for x = -2, -1, 0, 1, 2.
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Determine the values of F(x) = (x + 2)^2 for x = -4, -3, -2, -1, 0.
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Study Notes
Rigid Transformation
- Transformations that do not alter the shape of the graph are known as rigid transformations.
Parabola in Standard Position
- The vertex of a parabola in standard position is located at the coordinate point (0,0).
Parent Function of a Parabola
- The equation representing the parent function of a parabola in standard position is f(x) = x².
Vertical Translation
- The function f(x) = x² + 4 indicates a vertical translation of the parabola upward by 4 units.
Horizontal Translation
- The function f(x) = (x + 1)² represents a horizontal translation of the parabola to the left by 1 unit.
Vertical Stretch
- The function F(x) = 12x² shows a vertical stretch of the parabola due to the coefficient 12, making it narrower.
Vertical Reflection
- The function F(x) = -x² reflects the parabola vertically across the x-axis due to the negative coefficient.
Vertical Compression
- The function F(x) = (1/5)x² illustrates a vertical compression of the parabola, as it stretches out due to the coefficient being less than 1.
Specific Function Values
- For the function F(x) = x² - 3, the values of x and their corresponding F(x) outputs are:
- x = -2, F(x) = 1
- x = -1, F(x) = -2
- x = 0, F(x) = -3
- x = 1, F(x) = -2
- x = 2, F(x) = 1
Additional Specific Function Values
- For the function F(x) = (x + 2)², the values of x and their corresponding F(x) outputs are:
- x = -4, F(x) = 4
- x = -3, F(x) = 1
- x = -2, F(x) = 0
- x = -1, F(x) = 1
- x = 0, F(x) = 4
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Test your knowledge of algebraic transformations and parabolas with these flashcards. This quiz covers rigid transformations, vertex positions, and parent functions. Perfect for reinforcing your understanding of foundational algebra concepts.
