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
![**Transcription and Explanation for Educational Website**
**Text:**
"Write the function graphed below in vertex form."
**Graph Description:**
The graph depicts a parabola in a coordinate plane. The parabola opens downwards and is symmetrical about a vertical line. It appears to have its vertex at the point (1, 8). The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10. The grid lines are evenly spaced.
**Key Features:**
- **Vertex:** The highest point or vertex of the parabola is at (1, 8).
- **Direction:** The parabola opens downwards, indicating the coefficient of the squared term in its equation is negative.
- **Axis of Symmetry:** The vertical line x = 1 serves as the axis of symmetry for the parabola.
**Objective:**
The task is to write the quadratic function representing this parabola in vertex form. The vertex form of a quadratic equation is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
**Solution Approach:**
1. Identify the vertex \((h, k) = (1, 8)\).
2. Determine the value of \(a\) by considering the vertical stretch and direction (opening downwards suggests \(a\) is negative).
3. Use the vertex form formula to write the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa658fe65-06ca-4677-a67f-37eb77e50c99%2F1365bd38-7d5f-4110-8314-2f261763153f%2Fai9hq1n_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Website**
**Text:**
"Write the function graphed below in vertex form."
**Graph Description:**
The graph depicts a parabola in a coordinate plane. The parabola opens downwards and is symmetrical about a vertical line. It appears to have its vertex at the point (1, 8). The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10. The grid lines are evenly spaced.
**Key Features:**
- **Vertex:** The highest point or vertex of the parabola is at (1, 8).
- **Direction:** The parabola opens downwards, indicating the coefficient of the squared term in its equation is negative.
- **Axis of Symmetry:** The vertical line x = 1 serves as the axis of symmetry for the parabola.
**Objective:**
The task is to write the quadratic function representing this parabola in vertex form. The vertex form of a quadratic equation is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
**Solution Approach:**
1. Identify the vertex \((h, k) = (1, 8)\).
2. Determine the value of \(a\) by considering the vertical stretch and direction (opening downwards suggests \(a\) is negative).
3. Use the vertex form formula to write the equation.
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