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The graph of a quadratic function f(x) = ax2 + bx + c is shown below. y X 4 6 8 10 -5 - 10 (a) The x-intercepts are (Enter your answers as a comma-separated list.) (b) The discriminant of the equation ax² + bx + c = 0 is positive (c) The solution(s) to the equation ax2 + bx + c = 0 is (are) (Enter your answers as a comma-separated list.)

The graph of a quadratic function f(x) = ax2 + bx + c is shown below. y X 4 6 8 10 -5 - 10 (a) The x-intercepts are (Enter your answers as a comma-separated list.) (b) The discriminant of the equation ax² + bx + c = 0 is positive (c) The solution(s) to the equation ax2 + bx + c = 0 is (are) (Enter your answers as a comma-separated list.)

Calculus: Early Transcendentals
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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### Quadratic Functions and Their Graphs The graph of a quadratic function \( f(x) = ax^2 + bx + c \) is depicted below: **Graph Analysis:** - **Axes**: The horizontal axis is labeled 'x' and the vertical axis is labeled 'y'. - **Parabola**: The graph shows a downward-opening parabola starting at approximately \( (0, 10) \) on the y-axis, bending down and reaching its minimum point just above the x-axis near \( x = 3 \), and then curving upwards beyond \( x = 5 \). - **X-Intercepts**: The parabola crosses the x-axis at two points, around \( x = 1 \) and \( x = 5 \). **Exercises:** (a) **X-Intercepts**:     Identify the x-intercepts of the parabola. These are the points where the graph meets the x-axis.     \( \text{The x-intercepts are } \_\_\_\_. \) *(Enter your answers as a comma-separated list.)* (b) **Discriminant**:     The discriminant of the equation \( ax^2 + bx + c = 0 \) determines the nature of the roots. In this case, the discriminant is:     \( \text{The discriminant is } \textbf{positive} \). (c) **Solutions**:     Find the solutions to the equation \( ax^2 + bx + c = 0 \) based on the graph.     \( \text{The solution(s) to the equation are } \_\_\_\_. \) *(Enter your answers as a comma-separated list.)* Understanding the graph and identifying these components are crucial skills in analyzing quadratic functions.
Transcribed Image Text:### Quadratic Functions and Their Graphs The graph of a quadratic function \( f(x) = ax^2 + bx + c \) is depicted below: **Graph Analysis:** - **Axes**: The horizontal axis is labeled 'x' and the vertical axis is labeled 'y'. - **Parabola**: The graph shows a downward-opening parabola starting at approximately \( (0, 10) \) on the y-axis, bending down and reaching its minimum point just above the x-axis near \( x = 3 \), and then curving upwards beyond \( x = 5 \). - **X-Intercepts**: The parabola crosses the x-axis at two points, around \( x = 1 \) and \( x = 5 \). **Exercises:** (a) **X-Intercepts**:     Identify the x-intercepts of the parabola. These are the points where the graph meets the x-axis.     \( \text{The x-intercepts are } \_\_\_\_. \) *(Enter your answers as a comma-separated list.)* (b) **Discriminant**:     The discriminant of the equation \( ax^2 + bx + c = 0 \) determines the nature of the roots. In this case, the discriminant is:     \( \text{The discriminant is } \textbf{positive} \). (c) **Solutions**:     Find the solutions to the equation \( ax^2 + bx + c = 0 \) based on the graph.     \( \text{The solution(s) to the equation are } \_\_\_\_. \) *(Enter your answers as a comma-separated list.)* Understanding the graph and identifying these components are crucial skills in analyzing quadratic functions.
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