### Graphing the Function f(x) = x² - 10#### Task:**Graph the following function:**\[ f(x) = x^2 - 10 \]**Instructions:**Use the graphing tool to plot the function.---**Graph Description:**- The graph is displayed on a Cartesian coordinate system.- The x-axis ranges from -20 to 20, increasing in increments of 4 units.- The y-axis ranges from -20 to 20, increasing in increments of 4 units.- A rectangular grid covers the graph, aiding in precise plotting, with minor grid lines spaced at 1 unit intervals. **Graphing Tool:**To interact with the graph, use the "Click to enlarge graph" button, which provides a zoomed-in, detailed view for easier manipulation and inspection.This platform requires utilizing the provided graphing tool to plot the quadratic function accurately. Ensure each crucial point on the graph is correctly identified, focusing especially on the vertex of the parabola and its intersection with the y-axis. ### Interactive Parabola Editing Tool**Instruction for Use:**Use the provided interactions to edit the selected curve in the graph. This educational tool allows you to manipulate the shape and position of a parabola on a Cartesian plane.**Graph Explanation:**- **Axes:** The graph displays a Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) axes, ranging from -20 to 20 with grid lines denoting intervals of 2 units.- **Curve:** An orange parabola is currently plotted on the grid, opening upwards with its vertex on the y-axis near the point (0,4).**Modification Panel:**Located to the right of the graph, the panel provides several tools for manipulating the curve:- **Icons:** - **Pen Tool:** Select to manually draw a curve. - **Eraser Tool:** Use to erase portions of the drawn curve. - **Curve Tool:** Select to change the form of the curve. - **Undo Button:** Reverts the last action taken. - **Delete Button:** Removes the current curve. - **Clear Button:** Clears all drawn curves from the graph. - **Help Button:** Access additional help and guidance.**Transformation Controls:**A smaller window labeled with "Vertical Stretch," "Horizontal Stretch," "Vertical Shift," and "Horizontal Shift" allows precise adjustments through numerical input:- **Vertical Stretch:** Affects the curve's height. Inputting a value greater than 1 stretches the parabola vertically, while a value between 0 and 1 compresses it.- **Horizontal Stretch:** Modifies the curve's width. Values greater than 1 compress horizontally, while values between 0 and 1 stretch horizontally.- **Vertical Shift:** Moves the curve up or down on the y-axis.- **Horizontal Shift:** Moves the curve left or right on the x-axis.- **x-Reflection:** Reflects the curve across the y-axis when selected.- **y-Reflection:** Reflects the curve across the x-axis when selected.**Action Buttons:**- **Save:** Apply and save the current configuration of the curve.- **Cancel:** Discard changes and revert to the default or previous state.Feel free to experiment with these controls to understand how different transformations affect the shape and position of the parabola. This hands-on approach enhances comprehension of quadratic functions and their graphical representations.

Answered: Image /qna-images/answer/f9bcc5cd-3cfc-42f7-83e3-0f4d6efbf6c0.jpg

Answered: Graph the following function. f(x) = x2…

Math

Algebra

Graph the following function. f(x) = x2 – 10 Use the graphing tool to graph the function. Click to enlarge graph

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

### Graphing the Function f(x) = x² - 10

#### Task:
**Graph the following function:**

\[ f(x) = x^2 - 10 \]

**Instructions:**
Use the graphing tool to plot the function.

---

**Graph Description:**

- The graph is displayed on a Cartesian coordinate system.
- The x-axis ranges from -20 to 20, increasing in increments of 4 units.
- The y-axis ranges from -20 to 20, increasing in increments of 4 units.
- A rectangular grid covers the graph, aiding in precise plotting, with minor grid lines spaced at 1 unit intervals.

**Graphing Tool:**
To interact with the graph, use the "Click to enlarge graph" button, which provides a zoomed-in, detailed view for easier manipulation and inspection.

This platform requires utilizing the provided graphing tool to plot the quadratic function accurately. Ensure each crucial point on the graph is correctly identified, focusing especially on the vertex of the parabola and its intersection with the y-axis.

### Interactive Parabola Editing Tool

**Instruction for Use:**
Use the provided interactions to edit the selected curve in the graph. This educational tool allows you to manipulate the shape and position of a parabola on a Cartesian plane.

**Graph Explanation:**
- **Axes:** The graph displays a Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) axes, ranging from -20 to 20 with grid lines denoting intervals of 2 units.
- **Curve:** An orange parabola is currently plotted on the grid, opening upwards with its vertex on the y-axis near the point (0,4).

**Modification Panel:**
Located to the right of the graph, the panel provides several tools for manipulating the curve:
- **Icons:**
- **Pen Tool:** Select to manually draw a curve.
- **Eraser Tool:** Use to erase portions of the drawn curve.
- **Curve Tool:** Select to change the form of the curve.
- **Undo Button:** Reverts the last action taken.
- **Delete Button:** Removes the current curve.
- **Clear Button:** Clears all drawn curves from the graph.
- **Help Button:** Access additional help and guidance.

**Transformation Controls:**
A smaller window labeled with "Vertical Stretch," "Horizontal Stretch," "Vertical Shift," and "Horizontal Shift" allows precise adjustments through numerical input:
- **Vertical Stretch:** Affects the curve's height. Inputting a value greater than 1 stretches the parabola vertically, while a value between 0 and 1 compresses it.
- **Horizontal Stretch:** Modifies the curve's width. Values greater than 1 compress horizontally, while values between 0 and 1 stretch horizontally.
- **Vertical Shift:** Moves the curve up or down on the y-axis.
- **Horizontal Shift:** Moves the curve left or right on the x-axis.
- **x-Reflection:** Reflects the curve across the y-axis when selected.
- **y-Reflection:** Reflects the curve across the x-axis when selected.

**Action Buttons:**
- **Save:** Apply and save the current configuration of the curve.
- **Cancel:** Discard changes and revert to the default or previous state.

Feel free to experiment with these controls to understand how different transformations affect the shape and position of the parabola. This hands-on approach enhances comprehension of quadratic functions and their graphical representations.

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