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 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=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 minus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

1 answer

To determine the parent function and the equation of the transformed function, we first need to identify the parent function for a parabola, which is typically represented as:

Parent function: \( y = x^2 \)

Next, to find the transformed function, we look for changes that have been applied to the parent function, such as translations or reflections.

From the options provided and given that there is a "+2" involved, we can deduce that if the graph is shifted to the left by 2 units, the transformed function would be:

Transformed function: \( y = (x + 2)^2 \)

This implies that the correct response would be:

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

Thus, the correct choice is:

The parent function is y=x². The equation of the transformed function is y=(x+2)².