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f(x)=2(x-4)² +2 Parent: Transformations:

f(x)=2(x-4)² +2 Parent: Transformations:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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can anyone state the equation of the parent function and state the transformations in proper order please
**Function and Transformations** The given function is: \[ f(x) = 2(x - 4)^2 + 2 \] **Parent Function:** The parent function for this quadratic function is: \[ f(x) = x^2 \] **Transformations:** 1. **Horizontal Shift**: The function \( (x - 4) \) inside the squared term indicates a horizontal shift. Here, it moves the graph to the right by 4 units. 2. **Vertical Stretch**: The coefficient 2 outside the squared term (multiplied by the squared term) is a vertical stretch of the graph by a factor of 2. 3. **Vertical Shift**: The constant term +2 outside the squared term indicates a vertical shift upwards by 2 units. In summary, the graph of the original parent function \( f(x) = x^2 \) is horizontally shifted 4 units to the right, vertically stretched by a factor of 2, and then shifted upwards by 2 units to obtain the graph of \( f(x) = 2(x - 4)^2 + 2 \).
Transcribed Image Text:**Function and Transformations** The given function is: \[ f(x) = 2(x - 4)^2 + 2 \] **Parent Function:** The parent function for this quadratic function is: \[ f(x) = x^2 \] **Transformations:** 1. **Horizontal Shift**: The function \( (x - 4) \) inside the squared term indicates a horizontal shift. Here, it moves the graph to the right by 4 units. 2. **Vertical Stretch**: The coefficient 2 outside the squared term (multiplied by the squared term) is a vertical stretch of the graph by a factor of 2. 3. **Vertical Shift**: The constant term +2 outside the squared term indicates a vertical shift upwards by 2 units. In summary, the graph of the original parent function \( f(x) = x^2 \) is horizontally shifted 4 units to the right, vertically stretched by a factor of 2, and then shifted upwards by 2 units to obtain the graph of \( f(x) = 2(x - 4)^2 + 2 \).
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