**Title: Solving Equations Graphically****Problem Statement:**Which of the graphs below correctly solves for \( x \) in the equation \( -x^2 - 3x - 1 = -x - 4 \)?**Graph Analysis:**1. **First Graph:** - **Axes:** The graph features a standard Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. - **Curves:** - A parabolic curve represented in blue. - A straight line represented in red. - **Key Points:** - The parabolic curve intersects the straight line at coordinates (0,2) and (-4,-2).2. **Second Graph:** - **Axes:** The graph features a similar standard Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. - **Curves:** - A parabolic curve represented in blue. - A straight line represented in red. - **Key Points:** - The parabolic curve intersects the straight line at coordinates (0,2) and (4,6). ### Graph Analysis on an Educational Website#### Graph 1:The first graph features two distinct curves: a blue parabola and a red line. Both curves are plotted against an X-Y coordinate plane with grid lines.- **Blue Parabola**: This quadratic curve opens downwards, suggesting it has a maximum point. The blue line intersects the Y-axis at approximately -1 and -3. - **Intercepts and Specific Points**: - The graph passes through the points \((-3, -1)\) and \((1, -5)\), highlighting key points of intersection or specific plotted values on the parabola.- **Red Line**: This line appears diagonal, cutting across the coordinate plane from the top left to the bottom right, indicating a negative slope. The intersection of the red line and blue parabola showcases potential solutions to a system of equations where both equations are satisfied.#### Graph 2:The second graph also features two curves: another blue parabola and a red line, again plotted on an X-Y coordinate plane.- **Blue Parabola**: This quadratic curve opens upwards this time, indicating a minimum point in the parabola’s structure. The parabola intersects the Y-axis at several points. - **Specific Points**: - Highlighted in the graph is the point \((2, 0)\), suggesting an important intersection or root of the equation.- **Red Line**: Similarly, this line is diagonal and crosses the coordinate plane from the lower left to the upper right, indicating a positive slope.The intersection points between the red line and the blue parabola are significant in solving a system of equations represented by these two distinct functions. Both graphs visually represent the system of equations and their solutions, providing insights into the behavior of quadratic and linear relationships on a coordinate grid.

Answered: Image /qna-images/answer/57256426-4b77-4483-9d90-56e3d0a3946d.jpg

Answered: Which of the graphs below correctly…

Which of the graphs below correctly solves for x in the equation -x²-3x - 1 = -x-4? 10 A O -10-8-6 (-4,-2) 8 6 (0,2) 2 2 4 6 8 10 B W (4, 6) (0,2) -10-8-6 -4 -2 Z -2 2 4 6 8 10

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Title: Solving Equations Graphically**

**Problem Statement:**
Which of the graphs below correctly solves for \( x \) in the equation \( -x^2 - 3x - 1 = -x - 4 \)?

**Graph Analysis:**

1. **First Graph:**
- **Axes:** The graph features a standard Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10.
- **Curves:**
- A parabolic curve represented in blue.
- A straight line represented in red.
- **Key Points:**
- The parabolic curve intersects the straight line at coordinates (0,2) and (-4,-2).

2. **Second Graph:**
- **Axes:** The graph features a similar standard Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10.
- **Curves:**
- A parabolic curve represented in blue.
- A straight line represented in red.
- **Key Points:**
- The parabolic curve intersects the straight line at coordinates (0,2) and (4,6).

### Graph Analysis on an Educational Website

#### Graph 1:

The first graph features two distinct curves: a blue parabola and a red line. Both curves are plotted against an X-Y coordinate plane with grid lines.

- **Blue Parabola**: This quadratic curve opens downwards, suggesting it has a maximum point. The blue line intersects the Y-axis at approximately -1 and -3.
- **Intercepts and Specific Points**:
- The graph passes through the points \((-3, -1)\) and \((1, -5)\), highlighting key points of intersection or specific plotted values on the parabola.

- **Red Line**: This line appears diagonal, cutting across the coordinate plane from the top left to the bottom right, indicating a negative slope.

The intersection of the red line and blue parabola showcases potential solutions to a system of equations where both equations are satisfied.

#### Graph 2:

The second graph also features two curves: another blue parabola and a red line, again plotted on an X-Y coordinate plane.

- **Blue Parabola**: This quadratic curve opens upwards this time, indicating a minimum point in the parabola’s structure. The parabola intersects the Y-axis at several points.
- **Specific Points**:
- Highlighted in the graph is the point \((2, 0)\), suggesting an important intersection or root of the equation.

- **Red Line**: Similarly, this line is diagonal and crosses the coordinate plane from the lower left to the upper right, indicating a positive slope.

The intersection points between the red line and the blue parabola are significant in solving a system of equations represented by these two distinct functions.

Both graphs visually represent the system of equations and their solutions, providing insights into the behavior of quadratic and linear relationships on a coordinate grid.

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