Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![The image shows a question from a College Algebra section.
---
**Topic**: Graphing Quadratic Functions
**Question 6 of 19**
**Instructions**: Graph the following function.
\[ f(x) = 3(x - 2)^2 - 3 \]
**Additional Details**: There is a small icon suggesting a graph can be enlarged by clicking. The option selected is "none."
---
### Explanation:
The function given is a quadratic function in vertex form: \[ f(x) = a(x - h)^2 + k \]
- **\( a = 3 \)**: This indicates the parabola opens upwards and is vertically stretched by a factor of 3.
- **\( h = 2 \)**: This shifts the parabola 2 units to the right.
- **\( k = -3 \)**: This shifts the parabola 3 units downwards.
#### Graphing Steps:
1. Identify the vertex of the parabola at \( (h, k) = (2, -3) \).
2. Based on the value of \( a\), determine that the parabola is narrower than a standard parabola \( (a = 1)\).
3. Plot the vertex and use the value of \( a \) to find additional points to sketch the graph.
Students are encouraged to click on "Click to enlarge graph" to visualize the graph of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84f905e7-8d15-44f1-8ba1-68b7e3fd4c33%2F431c33a1-e77e-4910-8673-389ebcd9c315%2F7h9ivwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a question from a College Algebra section.
---
**Topic**: Graphing Quadratic Functions
**Question 6 of 19**
**Instructions**: Graph the following function.
\[ f(x) = 3(x - 2)^2 - 3 \]
**Additional Details**: There is a small icon suggesting a graph can be enlarged by clicking. The option selected is "none."
---
### Explanation:
The function given is a quadratic function in vertex form: \[ f(x) = a(x - h)^2 + k \]
- **\( a = 3 \)**: This indicates the parabola opens upwards and is vertically stretched by a factor of 3.
- **\( h = 2 \)**: This shifts the parabola 2 units to the right.
- **\( k = -3 \)**: This shifts the parabola 3 units downwards.
#### Graphing Steps:
1. Identify the vertex of the parabola at \( (h, k) = (2, -3) \).
2. Based on the value of \( a\), determine that the parabola is narrower than a standard parabola \( (a = 1)\).
3. Plot the vertex and use the value of \( a \) to find additional points to sketch the graph.
Students are encouraged to click on "Click to enlarge graph" to visualize the graph of the function.
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