**Transcription for Educational Website:**### Problem Description:"Write an equation (any form) for the quadratic graphed below."### Graph Analysis:The graph displayed is a parabola opening upwards. It intersects the y-axis at (0,1), and the x-axis at approximately (-1,0) and (3,0). The vertex of the parabola is at the minimum point, around (1,0).- **X-axis:** Ranges from -5 to 5- **Y-axis:** Ranges from -5 to 5- **Vertex:** (1, 0)- **Y-intercept:** (0, 1)### Task:Using the given graph, determine a possible equation for the quadratic function in any form (standard, vertex, or factored form).### Example Solution:To write the equation, recognize the vertex form of a quadratic function: \[ y = a(x - h)^2 + k \]where (h, k) is the vertex.Given the vertex (1,0), substitute into the vertex form:\[ y = a(x - 1)^2 \]To find "a", use another point from the graph, such as the y-intercept (0,1):\[ 1 = a(0 - 1)^2 \]\[ a = 1 \]Thus, the equation of the parabola could be:\[ y = (x - 1)^2 \]This is a potential equation based on the visible points on the graph. Other forms of the equation can be derived similarly.

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Algebra

WPite an equation (any form) for the quadratic graphed below -5 -4 -3 -2 -1 1 2 --2-

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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**Transcription for Educational Website:**

### Problem Description:

"Write an equation (any form) for the quadratic graphed below."

### Graph Analysis:

The graph displayed is a parabola opening upwards. It intersects the y-axis at (0,1), and the x-axis at approximately (-1,0) and (3,0). The vertex of the parabola is at the minimum point, around (1,0).

- **X-axis:** Ranges from -5 to 5
- **Y-axis:** Ranges from -5 to 5
- **Vertex:** (1, 0)
- **Y-intercept:** (0, 1)

### Task:

Using the given graph, determine a possible equation for the quadratic function in any form (standard, vertex, or factored form).

### Example Solution:

To write the equation, recognize the vertex form of a quadratic function:
\[ y = a(x - h)^2 + k \]
where (h, k) is the vertex.

Given the vertex (1,0), substitute into the vertex form:
\[ y = a(x - 1)^2 \]

To find "a", use another point from the graph, such as the y-intercept (0,1):
\[ 1 = a(0 - 1)^2 \]
\[ a = 1 \]

Thus, the equation of the parabola could be:
\[ y = (x - 1)^2 \]

This is a potential equation based on the visible points on the graph. Other forms of the equation can be derived similarly.

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