**Equations and Graphing Activity****Consider the Following Equations:**1. $ y = x^2 - 4 $2. $ y = -x + 3 $3. $ x = 0 $4. $ x = 2 $**Instructions:**1. Sketch and shade the region bounded by the graphs of the functions. Use solid lines for the boundaries.2. **Graph Details:** - The graph displays a coordinate grid with the x-axis ranging from -2 to 3 and the y-axis ranging from -5 to 10. - The quadratic function $ y = x^2 - 4 $ will form a parabola opening upwards with its vertex at (0, -4). - The linear function $ y = -x + 3 $ is a straight line with a y-intercept at (0, 3) and a slope of -1. - The vertical lines $ x = 0 $ and $ x = 2 $ will form boundaries for the shaded region on the graph.3. Use the graphing tools to accurately represent the functions and identify the bounded region.4. **Objective:** - Find the area of the shaded region.**Graph Layers:**- After you add an object to the graph, you can use Graph Layers to view and edit its properties.**Task:**- Complete the activity by determining the area of the region enclosed by the graphs.

Answered: Consider the following equations. y x-4…

Consider the following equations. y x-4 y = -x + 3 x = 0 x = 2 Sketch and shade the region bounded by the graphs of the functions. (Use solid lines for the boundaries.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Equations and Graphing Activity**

**Consider the Following Equations:**

1. $ y = x^2 - 4 $
2. $ y = -x + 3 $
3. $ x = 0 $
4. $ x = 2 $

**Instructions:**

1. Sketch and shade the region bounded by the graphs of the functions. Use solid lines for the boundaries.

2. **Graph Details:**
- The graph displays a coordinate grid with the x-axis ranging from -2 to 3 and the y-axis ranging from -5 to 10.
- The quadratic function $ y = x^2 - 4 $ will form a parabola opening upwards with its vertex at (0, -4).
- The linear function $ y = -x + 3 $ is a straight line with a y-intercept at (0, 3) and a slope of -1.
- The vertical lines $ x = 0 $ and $ x = 2 $ will form boundaries for the shaded region on the graph.

3. Use the graphing tools to accurately represent the functions and identify the bounded region.

4. **Objective:**
- Find the area of the shaded region.

**Graph Layers:**

- After you add an object to the graph, you can use Graph Layers to view and edit its properties.

**Task:**
- Complete the activity by determining the area of the region enclosed by the graphs.

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