**Sketching a Graph of a Quadratic Function**### Function Definition:The function given is a quadratic function defined as:\[ f(x) = (x - 2)^2 - 5 \]### Instructions:Use the graphing tool to sketch the function. ### Enlarging the Graph:There is an option to enlarge the graph by clicking the button labeled "Click to enlarge graph."### Graph Description:A coordinate plane is provided for graphing, with both the $x$-axis and the $y$-axis ranging from -10 to 10. The graph is displayed with a grid to help in plotting points accurately.### Notes:In red text under the instructions, it says "need explanations." This suggests providing detailed steps or guidance on how to plot the graph of the given quadratic function.### How to Plot:1. Identify the vertex of the parabola. For the given function $ f(x) = (x - 2)^2 - 5 $, the vertex is at the point $ (2, -5) $.2. Determine a few points around the vertex to get a more accurate graph. For example, calculate $ f(x) $ for $ x = 1 $, $ x = 0 $, $ x = 3 $, and $ x = 4 $.3. Reflect these points across the axis of symmetry, which is $ x = 2 $ in this case.4. Plot these points on the coordinate grid and draw a smooth curve through them to complete the graph of the parabola.**Understanding the Graph of the Function:**- The graph of $ f(x) = (x - 2)^2 - 5 $ will be a parabola opening upwards because the coefficient of $ (x - 2)^2 $ is positive.- The vertex $(2, -5)$ is the minimum point of the graph.- The axis of symmetry is the vertical line $ x = 2 $.- The graph should include several points to ensure it is shaped correctly, with the points symmetrically placed around the axis of symmetry.Using the graphing tool and the coordinate grid, visualize and plot the quadratic function carefully to understand its behavior and key features.

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Answered: Sketch a graph of f. Ay 10- f(x) = (x-…

Sketch a graph of f. Ay 10- f(x) = (x- 2)² – 5 8- Use the graphing tool to graph the function. 6- Click to 4- enlarge graph 2- heed explonedions 10 -8 -6 -4 -2- Loo

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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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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**Sketching a Graph of a Quadratic Function**

### Function Definition:
The function given is a quadratic function defined as:
\[ f(x) = (x - 2)^2 - 5 \]

### Instructions:
Use the graphing tool to sketch the function.

### Enlarging the Graph:
There is an option to enlarge the graph by clicking the button labeled "Click to enlarge graph."

### Graph Description:
A coordinate plane is provided for graphing, with both the $x$-axis and the $y$-axis ranging from -10 to 10. The graph is displayed with a grid to help in plotting points accurately.

### Notes:
In red text under the instructions, it says "need explanations." This suggests providing detailed steps or guidance on how to plot the graph of the given quadratic function.

### How to Plot:
1. Identify the vertex of the parabola. For the given function $ f(x) = (x - 2)^2 - 5 $, the vertex is at the point $ (2, -5) $.
2. Determine a few points around the vertex to get a more accurate graph. For example, calculate $ f(x) $ for $ x = 1 $, $ x = 0 $, $ x = 3 $, and $ x = 4 $.
3. Reflect these points across the axis of symmetry, which is $ x = 2 $ in this case.
4. Plot these points on the coordinate grid and draw a smooth curve through them to complete the graph of the parabola.

**Understanding the Graph of the Function:**
- The graph of $ f(x) = (x - 2)^2 - 5 $ will be a parabola opening upwards because the coefficient of $ (x - 2)^2 $ is positive.
- The vertex $(2, -5)$ is the minimum point of the graph.
- The axis of symmetry is the vertical line $ x = 2 $.
- The graph should include several points to ensure it is shaped correctly, with the points symmetrically placed around the axis of symmetry.

Using the graphing tool and the coordinate grid, visualize and plot the quadratic function carefully to understand its behavior and key features.

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