-6 -5 -4 -3 -2 -1 5 4 3 2 1 -2 -3 -4 -5 −6+ 1 2 3 4 5 6

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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In the graph the slope of the tangent at -1 is what?

The image displays a graph of a quadratic function, specifically a parabola. The parabola opens upwards and is centered around the vertex at the point (-1, -2). The graph is plotted on a coordinate plane with x- and y-axes ranging from -6 to 6.

### Key Features:

- **Vertex**: The lowest point of the parabola is at (-1, -2). This point is the vertex of the parabola.
- **Axis of Symmetry**: The line x = -1 is the axis of symmetry, meaning the parabola is symmetric around this vertical line.
- **Y-intercept**: The graph crosses the y-axis at a point, but this position is not marked, although it is evident that it will be somewhere above the vertex when extended.
- **X-intercepts**: The parabola intersects the x-axis between x = 0 and x = -2, suggesting that the x-intercepts are real and distinct.
- **Direction**: The parabola opens upwards, indicating that the quadratic coefficient is positive.

### Additional Observations:

The grid lines help visualize the curve more effectively, providing a clear understanding of the parabola's symmetry and intercepts. The graph illustrates the fundamental shape and orientation of a standard quadratic function.
Transcribed Image Text:The image displays a graph of a quadratic function, specifically a parabola. The parabola opens upwards and is centered around the vertex at the point (-1, -2). The graph is plotted on a coordinate plane with x- and y-axes ranging from -6 to 6. ### Key Features: - **Vertex**: The lowest point of the parabola is at (-1, -2). This point is the vertex of the parabola. - **Axis of Symmetry**: The line x = -1 is the axis of symmetry, meaning the parabola is symmetric around this vertical line. - **Y-intercept**: The graph crosses the y-axis at a point, but this position is not marked, although it is evident that it will be somewhere above the vertex when extended. - **X-intercepts**: The parabola intersects the x-axis between x = 0 and x = -2, suggesting that the x-intercepts are real and distinct. - **Direction**: The parabola opens upwards, indicating that the quadratic coefficient is positive. ### Additional Observations: The grid lines help visualize the curve more effectively, providing a clear understanding of the parabola's symmetry and intercepts. The graph illustrates the fundamental shape and orientation of a standard quadratic function.
Expert Solution
Step 1: Concept used in the solution

The slope of a line parallel to the X axis    is 0 .

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