Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**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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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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