Use the graph to answer the question.

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 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.

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.
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Answer 1

The parent function of a parabola is typically represented as \( y = x^2 \).

To determine the equation of the transformed function, we look for shifts and transformations indicated by the graph (which unfortunately isn't visible to me). However, based on the common transformations of parabolas, we can derive a few scenarios:

1. If the parabola opens upwards and is centered at a vertex shifted 2 units to the left, then the transformed function would be \( y = (x + 2)^2 \).
2. If the parabola opens upwards and is centered at a vertex shifted 2 units to the right, then the transformed function would be \( y = (x - 2)^2 \).

Given the options you provided, the most likely correct choice, if it shifts left by 2, would be:

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

If it shifts right by 2, then:

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

Please consider the specific graph you are looking at to determine which transformation applies.