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What is the total area of the blue color regions?

What is the total area of the blue color regions?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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What is the total area of the blue color regions?

The graph illustrates the quadratic equation \( y = 9 - x^2 \). **Details of the Graph:** - **Axes:** - The x-axis and y-axis intersect at the origin (0,0). - The x-axis is labeled horizontally from -5 to 5. - The y-axis is labeled vertically, from -9 to 9. - **Curve:** - The curve represents a downward-opening parabola. - The apex of the parabola is at the point (0,9), indicating the vertex. - It crosses the x-axis at points (-3,0) and (3,0), showing the roots of the equation. - **Shaded Region:** - There is a blue shaded region underneath the curve, from x = -3 to x = 3, extending vertically down to the x-axis. **Explanation:** The parabola represents the quadratic function \( y = 9 - x^2 \), which opens downwards with its vertex at the topmost point (0,9). The points where it intersects the x-axis are its real roots, at x = -3 and x = 3. The shaded area likely indicates the portion under the curve between these roots, possibly representing an integral or area calculation relevant to the function.
Transcribed Image Text:The graph illustrates the quadratic equation \( y = 9 - x^2 \). **Details of the Graph:** - **Axes:** - The x-axis and y-axis intersect at the origin (0,0). - The x-axis is labeled horizontally from -5 to 5. - The y-axis is labeled vertically, from -9 to 9. - **Curve:** - The curve represents a downward-opening parabola. - The apex of the parabola is at the point (0,9), indicating the vertex. - It crosses the x-axis at points (-3,0) and (3,0), showing the roots of the equation. - **Shaded Region:** - There is a blue shaded region underneath the curve, from x = -3 to x = 3, extending vertically down to the x-axis. **Explanation:** The parabola represents the quadratic function \( y = 9 - x^2 \), which opens downwards with its vertex at the topmost point (0,9). The points where it intersects the x-axis are its real roots, at x = -3 and x = 3. The shaded area likely indicates the portion under the curve between these roots, possibly representing an integral or area calculation relevant to the function.
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