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.

Given function is y=9-x2 and shaded region bounded from x=0 to x=4

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What is the total area of the blue color regions?

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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Question

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.

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