### Quadratic Functions and Their GraphsThe 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.

Answered: Image /qna-images/answer/13739226-8c00-48f3-9033-b89362173743.jpg

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

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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Question

### 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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