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Which statement is not supported by the graph shown? V The coefficient of ² in the equation of this quadratic function is positive. The roots of the quadratic function are 0 and 3. The vertex of the graph is (2, 1). The quadratic function graphed has no real solution.

Which statement is not supported by the graph shown? V The coefficient of ² in the equation of this quadratic function is positive. The roots of the quadratic function are 0 and 3. The vertex of the graph is (2, 1). The quadratic function graphed has no real solution.

Algebra and Trigonometry (6th Edition)
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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### Quadratic Functions and Graph Analysis **Question:** Which statement is *not* supported by the graph shown? **Graph Description:** A coordinate plane is displayed with an upward-opening parabola. The y-axis and x-axis are labeled with incremental tick marks. The parabola has roots (where it intersects the x-axis) at points 0 and 3. A notable point, which appears to be the vertex, is indicated at (1.5, -1), although the exact vertex isn't explicitly marked in the graph. **Options:** 1. The coefficient of \( x^2 \) in the equation of this quadratic function is positive. 2. The roots of the quadratic function are 0 and 3. 3. The vertex of the graph is (2, 1). 4. The quadratic function graphed has no real solution. **Analysis:** 1. **Coefficient of \( x^2 \):** - Since the parabola opens upwards, the coefficient of \( x^2 \) must be positive. 2. **Roots of the Function:** - The graph intersects the x-axis at x=0 and x=3, indicating the roots are 0 and 3. 3. **Vertex:** - The vertex is not at (2, 1) based on the graph. The actual vertex appears to be at (1.5, -1). 4. **Real Solutions:** - The quadratic function does have real solutions, as indicated by its x-axis intersections at 0 and 3. **Conclusion:** The statement that is *not* supported by the graph is: - The vertex of the graph is (2, 1).
Transcribed Image Text:### Quadratic Functions and Graph Analysis **Question:** Which statement is *not* supported by the graph shown? **Graph Description:** A coordinate plane is displayed with an upward-opening parabola. The y-axis and x-axis are labeled with incremental tick marks. The parabola has roots (where it intersects the x-axis) at points 0 and 3. A notable point, which appears to be the vertex, is indicated at (1.5, -1), although the exact vertex isn't explicitly marked in the graph. **Options:** 1. The coefficient of \( x^2 \) in the equation of this quadratic function is positive. 2. The roots of the quadratic function are 0 and 3. 3. The vertex of the graph is (2, 1). 4. The quadratic function graphed has no real solution. **Analysis:** 1. **Coefficient of \( x^2 \):** - Since the parabola opens upwards, the coefficient of \( x^2 \) must be positive. 2. **Roots of the Function:** - The graph intersects the x-axis at x=0 and x=3, indicating the roots are 0 and 3. 3. **Vertex:** - The vertex is not at (2, 1) based on the graph. The actual vertex appears to be at (1.5, -1). 4. **Real Solutions:** - The quadratic function does have real solutions, as indicated by its x-axis intersections at 0 and 3. **Conclusion:** The statement that is *not* supported by the graph is: - The vertex of the graph is (2, 1).
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