The graph of the function \( y = x^2 \) is shown below in blue. Write a formula for the graph of \( g(x) \), shown in red, which is the result of applying a sequence of transformations to the graph of \( y = x^2 \).**Graph Explanation:**1. **Blue Parabola**: Represents the function \( y = x^2 \). It is a typical upward-opening parabola centered at the origin (0,0).2. **Red Parabola**: Represents the function \( g(x) \), which is a transformation of the blue parabola. It is also an upward-opening parabola but shifted to the right. **Transformation Details:**- The red parabola appears to be the result of a horizontal shift of 2 units to the right of the blue parabola.**Conclusion:**To find the formula for \( g(x) \), apply a horizontal shift to the function \( y = x^2 \). The transformation results in the function \( g(x) = (x - 2)^2 \).\[ g(x) = \]

The graph of the function y = x2 is shown below in blue. Write a formula for the graph of g(x), 2?. shown in red, which is the result of applying a sequence of transformations to the graph of y 6+ 5- 4- 3- -6 -5 -4 -3 -2 -1 2 in

The graph of the function y = x2 is shown below in blue. Write a formula for the graph of g(x), 2?. shown in red, which is the result of applying a sequence of transformations to the graph of y 6+ 5- 4- 3- -6 -5 -4 -3 -2 -1 2 in

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 graph of the function \( y = x^2 \) is shown below in blue. Write a formula for the graph of \( g(x) \), shown in red, which is the result of applying a sequence of transformations to the graph of \( y = x^2 \).

**Graph Explanation:**

1. **Blue Parabola**: Represents the function \( y = x^2 \). It is a typical upward-opening parabola centered at the origin (0,0).

2. **Red Parabola**: Represents the function \( g(x) \), which is a transformation of the blue parabola. It is also an upward-opening parabola but shifted to the right.

**Transformation Details:**

- The red parabola appears to be the result of a horizontal shift of 2 units to the right of the blue parabola.

**Conclusion:**

To find the formula for \( g(x) \), apply a horizontal shift to the function \( y = x^2 \). The transformation results in the function \( g(x) = (x - 2)^2 \).

\[ g(x) = \]

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