**Graphing Exercise for Students**### Instructions:**2. Using your graphing calculator, sketch the graph of $ 2(x - 1)^2 + 2(y + 1)^2 = 6 $.**#### Editor- $ y_1 = $- $ y_2 = $#### Window\[ [ \ , \ ] \text{ by } [ \ , \ ] \]#### SketchProvide a clear sketch of the graph based on the given equation.### Detailed Explanation:To graph the equation given, follow these steps:1. **Rewrite the equation in a standard form:** \[ 2(x - 1)^2 + 2(y + 1)^2 = 6 \] Simplify: \[ (x - 1)^2 + (y + 1)^2 = 3 \] This equation represents a circle centered at $(1, -1)$ with a radius $\sqrt{3}$.2. **Enter the function in your graphing calculator:** - You may have to solve for $y$ and input two separate equations for the circle. For instance, \[ y_1 = -1 + \sqrt{3 - (x - 1)^2} \] \[ y_2 = -1 - \sqrt{3 - (x - 1)^2} \]3. **Set the window on your graphing calculator:** - Ensure your window settings appropriately capture the center and radius of the circle. - Example window settings might be: - Xmin: -2, Xmax: 4 - Ymin: -4, Ymax: 24. **Sketch the Graph:** - Use the graphing calculator to plot the circle and then replicate the circle on your paper.By following these steps, you will accurately sketch the given equation's graph and understand the graphical representation of circle equations.

The given quadratic equation is: This can also be written as: This equation represents the…

Answered: 2. Using your graphing calculator,…

Math

Algebra

2. Using your graphing calculator, sketch the graph of 2(x-1)² + 2(y+ 1)² =6. EDITOR

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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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

**Graphing Exercise for Students**

### Instructions:
**2. Using your graphing calculator, sketch the graph of $ 2(x - 1)^2 + 2(y + 1)^2 = 6 $.**

#### Editor
- $ y_1 = $
- $ y_2 = $

#### Window
\[ [ \ , \ ] \text{ by } [ \ , \ ] \]

#### Sketch
Provide a clear sketch of the graph based on the given equation.

### Detailed Explanation:

To graph the equation given, follow these steps:

1. **Rewrite the equation in a standard form:**
\[ 2(x - 1)^2 + 2(y + 1)^2 = 6 \]
Simplify: \[ (x - 1)^2 + (y + 1)^2 = 3 \]

This equation represents a circle centered at $(1, -1)$ with a radius $\sqrt{3}$.

2. **Enter the function in your graphing calculator:**
- You may have to solve for $y$ and input two separate equations for the circle. For instance,
\[ y_1 = -1 + \sqrt{3 - (x - 1)^2} \]
\[ y_2 = -1 - \sqrt{3 - (x - 1)^2} \]

3. **Set the window on your graphing calculator:**
- Ensure your window settings appropriately capture the center and radius of the circle.
- Example window settings might be:
- Xmin: -2, Xmax: 4
- Ymin: -4, Ymax: 2

4. **Sketch the Graph:**
- Use the graphing calculator to plot the circle and then replicate the circle on your paper.

By following these steps, you will accurately sketch the given equation's graph and understand the graphical representation of circle equations.

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