Question

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Analyzing a Graph Quick Check
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Question
Use the graph to answer the question.

A parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.


The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function.

(1 point)
Responses

The parent function is y=(x−2)2
. The equation of the transformed function is y=x2
.
The parent f unction is y is equal to open paren x minus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x minus 2 close paren squared.

The parent function is y=(x+2)2
. The equation of the transformed function is y=x2
.
The parent f unction is y is equal to open paren x plus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x plus 2 close paren squared.

Answers

Answered by GPT-4o mini
To determine the parent function and the equation of the transformed function based on the given information about a parabola, we first need to identify the characteristics of the graph.

1. The parent function of a parabola is typically \( y = x^2 \).
2. The transformed version of this function can involve translations, which would shift the graph horizontally and/or vertically.

From the options presented, we can analyze them based on the transformation:

- If the graph is shifted right by 2 units, the transformed function would be \( y = (x - 2)^2 \).
- If the graph is shifted left by 2 units, the transformed function would be \( y = (x + 2)^2 \).

Given these transformations, it seems likely that the correct answer is:

**The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x - 2)^2 \).**

This option implies the graph of the parabola has been shifted 2 units to the right, which is a common transformation for parabolas.

Thus, the final response would be:

**The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x - 2)^2 \).**

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