What is the equation of the given graph? 1:34 PM Tue Nov 10 43% 4 Untitled Graph desmos Save Javier 10 >> (-3,523, 2.756) (-4, 0) (-3,0) (2,0) -10 -8 -6 -2 8 --10 -20 -30 -40 (0.189, -48.385) |(0, -48) powered by desmos III

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 s the equation of this graph

**Title:** What is the equation of the given graph?

**Graph Description:**
The graph is a plot of a polynomial function with a cubic equation. It features a smooth curve that crosses the x-axis at three distinct points, indicating real roots.

**Key Points on the Graph:**
1. **X-Intercepts:** These are the points where the graph crosses the x-axis. The x-intercepts are labeled as:
   - \((-4, 0)\)
   - \((-3, 0)\)
   - \((2, 0)\)

2. **Y-Intercept:** The point where the graph crosses the y-axis is:
   - \((0, -48)\)

3. **Local Maximum:** The graph reaches a local maximum at:
   - \((-3.523, 2.756)\)

4. **Local Minimum:** The graph reaches a local minimum at:
   - \((0.189, -48.385)\)

The graph displays a classic cubic behavior, with an upward trend on both ends while dipping in the center, which is characteristic of a function with three real roots and two turning points.

**Equation Format:**
Based on the x-intercepts, the equation of the graph can be assumed to have a factorized form. To find the particular equation, one can set it based on these intercepts: \( f(x) = a(x + 4)(x + 3)(x - 2) \). The \(a\) value can be determined using the y-intercept.

**Note:** To ensure accuracy and explore the exact equation further, consider the graph's dynamic behavior and explore different functions using graphing tools such as Desmos.
Transcribed Image Text:**Title:** What is the equation of the given graph? **Graph Description:** The graph is a plot of a polynomial function with a cubic equation. It features a smooth curve that crosses the x-axis at three distinct points, indicating real roots. **Key Points on the Graph:** 1. **X-Intercepts:** These are the points where the graph crosses the x-axis. The x-intercepts are labeled as: - \((-4, 0)\) - \((-3, 0)\) - \((2, 0)\) 2. **Y-Intercept:** The point where the graph crosses the y-axis is: - \((0, -48)\) 3. **Local Maximum:** The graph reaches a local maximum at: - \((-3.523, 2.756)\) 4. **Local Minimum:** The graph reaches a local minimum at: - \((0.189, -48.385)\) The graph displays a classic cubic behavior, with an upward trend on both ends while dipping in the center, which is characteristic of a function with three real roots and two turning points. **Equation Format:** Based on the x-intercepts, the equation of the graph can be assumed to have a factorized form. To find the particular equation, one can set it based on these intercepts: \( f(x) = a(x + 4)(x + 3)(x - 2) \). The \(a\) value can be determined using the y-intercept. **Note:** To ensure accuracy and explore the exact equation further, consider the graph's dynamic behavior and explore different functions using graphing tools such as Desmos.
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