Homework Help is Here – Start Your Trial Now!
Math
Algebra
Match the function with the graph. A) g(x) = (x-4)² -10 B) g(x) = x² + 4 10 x C) g(x)=x²-4 D) g(x) = (x + 4)²

Match the function with the graph. A) g(x) = (x-4)² -10 B) g(x) = x² + 4 10 x C) g(x)=x²-4 D) g(x) = (x + 4)²

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section: Chapter Questions
Problem 74SGR
See similar textbooks
icon
Related questions
Question

Need to know how to show work for the problem attached

### Match the Function with the Graph Below is a task to match the function with its corresponding graph based on the given options. #### Functions: A) \( g(x) = \frac{1}{3}(x - 4)^2 \) B) \( g(x) = \frac{1}{3}x^2 + 4 \) C) \( g(x) = \frac{1}{3}x^2 - 4 \) D) \( g(x) = (x + 4)^2 \) #### Graph Explanation: In the middle of the image is a coordinate plane with the x-axis and y-axis ranging from -10 to 10. There is one parabola graphed which opens upwards and has a vertex at the point (0, -4). #### Visual Analysis of the Graph: 1. **Vertex Identification**: The vertex of the parabola appears to be on the y-axis at (0, -4). 2. **Opening Direction**: The parabola opens upwards, indicating a positive leading coefficient. Given this information: - Option A \(\left( g(x) = \frac{1}{3}(x - 4)^2 \right)\) shifts the graph to the right. - Option B \(\left( g(x) = \frac{1}{3}x^2 + 4 \right)\) shifts the graph upwards. - Option D \(\left( g(x) = (x + 4)^2 \right)\) shifts the graph to the left. - Option C \(\left( g(x) = \frac{1}{3}x^2 - 4 \right)\) shifts the graph downwards by 4 units. Considering the graph provided, the correct function that matches the graph is: **C) \( g(x) = \frac{1}{3}x^2 - 4 \)** The graph shows a parabola opening upwards with a vertex at (0, -4), which corresponds to the function \( g(x) = \frac{1}{3}x^2 - 4 \).
Transcribed Image Text:### Match the Function with the Graph Below is a task to match the function with its corresponding graph based on the given options. #### Functions: A) \( g(x) = \frac{1}{3}(x - 4)^2 \) B) \( g(x) = \frac{1}{3}x^2 + 4 \) C) \( g(x) = \frac{1}{3}x^2 - 4 \) D) \( g(x) = (x + 4)^2 \) #### Graph Explanation: In the middle of the image is a coordinate plane with the x-axis and y-axis ranging from -10 to 10. There is one parabola graphed which opens upwards and has a vertex at the point (0, -4). #### Visual Analysis of the Graph: 1. **Vertex Identification**: The vertex of the parabola appears to be on the y-axis at (0, -4). 2. **Opening Direction**: The parabola opens upwards, indicating a positive leading coefficient. Given this information: - Option A \(\left( g(x) = \frac{1}{3}(x - 4)^2 \right)\) shifts the graph to the right. - Option B \(\left( g(x) = \frac{1}{3}x^2 + 4 \right)\) shifts the graph upwards. - Option D \(\left( g(x) = (x + 4)^2 \right)\) shifts the graph to the left. - Option C \(\left( g(x) = \frac{1}{3}x^2 - 4 \right)\) shifts the graph downwards by 4 units. Considering the graph provided, the correct function that matches the graph is: **C) \( g(x) = \frac{1}{3}x^2 - 4 \)** The graph shows a parabola opening upwards with a vertex at (0, -4), which corresponds to the function \( g(x) = \frac{1}{3}x^2 - 4 \).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS