Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question

Find a quadratic equation for the parabola below. Use the points (0,4), (1,1), and (4,4)

You have to show:

  1. the system of three equations
  2. matrix 
  3. your answers for the parameters a,b, and c. Round your answers to three decimal places. 
  4. your final equation y= 

 

 

 

**Graph Description: Quadratic Function** This graph illustrates a quadratic function represented by a parabola that opens upwards. ### Key Features: 1. **Axes**: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). 2. **Parabola**: - The curve intersects the x-axis at the point (2, 0) which is the vertex of the parabola, indicating it is the minimum point of the function. - The parabola is symmetrical around the vertical line \( x = 2 \), which is the axis of symmetry for this function. 3. **Points**: - The points (0, 4) and (4, 4) lie on the parabola, indicating symmetry about the axis \( x = 2 \). - The points (1, 1) and (3, 1) show additional symmetric points on the parabola. 4. **Line of Symmetry**: - A dotted vertical line at \( x = 2 \) represents the line of symmetry for the parabola. 5. **Origin**: The graph includes the origin point \( O \) at (0, 0). This graph can be used to demonstrate properties such as symmetry, vertex, and intercepts of quadratic functions in an educational context.
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Transcribed Image Text:**Graph Description: Quadratic Function** This graph illustrates a quadratic function represented by a parabola that opens upwards. ### Key Features: 1. **Axes**: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). 2. **Parabola**: - The curve intersects the x-axis at the point (2, 0) which is the vertex of the parabola, indicating it is the minimum point of the function. - The parabola is symmetrical around the vertical line \( x = 2 \), which is the axis of symmetry for this function. 3. **Points**: - The points (0, 4) and (4, 4) lie on the parabola, indicating symmetry about the axis \( x = 2 \). - The points (1, 1) and (3, 1) show additional symmetric points on the parabola. 4. **Line of Symmetry**: - A dotted vertical line at \( x = 2 \) represents the line of symmetry for the parabola. 5. **Origin**: The graph includes the origin point \( O \) at (0, 0). This graph can be used to demonstrate properties such as symmetry, vertex, and intercepts of quadratic functions in an educational context.
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