Graph shown is a translation of the graph of f(x)=x2. Write the function in vertex form. ### Graph of a Parabolic FunctionThis image illustrates the graph of a parabolic function in a Cartesian coordinate system.#### Key Features1. **Axes**: - The horizontal axis is labeled as \( x \) and the vertical axis is labeled as \( y \). - The origin \( O \) is indicated where the \( x \)-axis and \( y \)-axis intersect (0,0).2. **Grid**: - The graph features a grid with evenly spaced lines, aiding in identifying precise coordinates.3. **Parabola**: - The graph depicts a parabola that opens upwards. - The vertex, the lowest point of the parabola, is positioned at coordinate (2,0). This is marked with a red dot. - The parabola passes through the points (0,4) and (4,4). 4. **Arrows**: - There are arrowheads at the upper ends of the parabola, indicating that the parabola continues infinitely in the upward direction. This graph represents a quadratic function, typically expressed in the form \( y = a(x-h)^2+k \). For this specific graph, it appears to be centered at \( (h,k) = (2,0) \) with a positive \( a \) value, suggesting the function could be modeled by \( y = (x-2)^2 \).Understanding this graph is crucial for grasping the behavior of quadratic functions, which are fundamental in various fields such as physics, engineering, and economics. This particular depiction is useful for visualizing how the parabola translates and scales based on its equation.

Answered: Image /qna-images/answer/aefdfb60-414c-4c9b-80bd-160eef3bdd0b.jpg

Answered: Ту 6 2 2 4 X

Math

Algebra

Ту 6 2 2 4 X

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

Graph shown is a translation of the graph of f(x)=x². Write the function in vertex form.

### Graph of a Parabolic Function

This image illustrates the graph of a parabolic function in a Cartesian coordinate system.

#### Key Features

1. **Axes**:
- The horizontal axis is labeled as \( x \) and the vertical axis is labeled as \( y \).
- The origin \( O \) is indicated where the \( x \)-axis and \( y \)-axis intersect (0,0).

2. **Grid**:
- The graph features a grid with evenly spaced lines, aiding in identifying precise coordinates.

3. **Parabola**:
- The graph depicts a parabola that opens upwards.
- The vertex, the lowest point of the parabola, is positioned at coordinate (2,0). This is marked with a red dot.
- The parabola passes through the points (0,4) and (4,4).

4. **Arrows**:
- There are arrowheads at the upper ends of the parabola, indicating that the parabola continues infinitely in the upward direction.

This graph represents a quadratic function, typically expressed in the form \( y = a(x-h)^2+k \). For this specific graph, it appears to be centered at \( (h,k) = (2,0) \) with a positive \( a \) value, suggesting the function could be modeled by \( y = (x-2)^2 \).

Understanding this graph is crucial for grasping the behavior of quadratic functions, which are fundamental in various fields such as physics, engineering, and economics. This particular depiction is useful for visualizing how the parabola translates and scales based on its equation.

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