X interxepts of the graph when f(x)=0Smaller x value and larger x value **Graphing Quadratic Functions****Objective:**Use a graphing utility to graph the quadratic function.**Function to Graph:**\[ f(x) = x^2 - 9x - 22\]**Explanation of the Graph:**The graph shown is a plot of the quadratic function $ f(x) = x^2 - 9x - 22 $.### Key Elements:1. **Axes:** - The horizontal axis (x-axis) represents the variable $ x $, with values ranging from approximately -60 to 60. - The vertical axis (y-axis or $ f(x) $-axis) represents the function values, with markers at intervals of 20 (e.g., -100, -80, -60, -40, -20, 0, 20, 40, 60).2. **Quadratic Curve:** - The reddish curve represents the graph of the quadratic function. - The curve is a parabola that opens upwards because the coefficient of $ x^2 $ is positive. - This parabola demonstrates the typical U-shape associated with quadratic functions.### Analyzing the Graph:- **Vertex:** - The vertex of the parabola is the lowest point on the graph. - This point represents the minimum value of the quadratic function.- **Axis of Symmetry:** - The axis of symmetry of the parabola goes through the vertex and is a vertical line. For this graph, it is approximately at $ x = 4.5 $. - **Intercepts:** - **x-Intercepts:** - The points where the parabola crosses the x-axis represent the roots or solutions of the quadratic equation $ x^2 - 9x - 22 = 0 $. - **y-Intercept:** - The point where the parabola crosses the y-axis represents the value of the function when $ x = 0 $. Here, it is $ f(0) = -22 $.Use your graphing utility or graphing calculator to further explore the roots and behavior of this function, as observing changes to the coefficients can help deepen your understanding of quadratic functions.

Given that, The function is fx=x2-9x-22. For x-intercepts, when fx=0. Calculate the smaller value of…

Answered: Use a graphing utility to graph the…

Math

Algebra

Use a graphing utility to graph the quadratic function. f(x)=x²-9x-22 f(x) -60 40 60 40 20 40 60 MAI

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

X interxepts of the graph when f(x)=0 Smaller x value and larger x value

**Graphing Quadratic Functions**

**Objective:**
Use a graphing utility to graph the quadratic function.

**Function to Graph:**

\[
f(x) = x^2 - 9x - 22
\]

**Explanation of the Graph:**

The graph shown is a plot of the quadratic function $ f(x) = x^2 - 9x - 22 $.

### Key Elements:
1. **Axes:**
- The horizontal axis (x-axis) represents the variable $ x $, with values ranging from approximately -60 to 60.
- The vertical axis (y-axis or $ f(x) $-axis) represents the function values, with markers at intervals of 20 (e.g., -100, -80, -60, -40, -20, 0, 20, 40, 60).

2. **Quadratic Curve:**
- The reddish curve represents the graph of the quadratic function.
- The curve is a parabola that opens upwards because the coefficient of $ x^2 $ is positive.
- This parabola demonstrates the typical U-shape associated with quadratic functions.

### Analyzing the Graph:
- **Vertex:**
- The vertex of the parabola is the lowest point on the graph.
- This point represents the minimum value of the quadratic function.

- **Axis of Symmetry:**
- The axis of symmetry of the parabola goes through the vertex and is a vertical line. For this graph, it is approximately at $ x = 4.5 $.

- **Intercepts:**
- **x-Intercepts:**
- The points where the parabola crosses the x-axis represent the roots or solutions of the quadratic equation $ x^2 - 9x - 22 = 0 $.
- **y-Intercept:**
- The point where the parabola crosses the y-axis represents the value of the function when $ x = 0 $. Here, it is $ f(0) = -22 $.

Use your graphing utility or graphing calculator to further explore the roots and behavior of this function, as observing changes to the coefficients can help deepen your understanding of quadratic functions.

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