Question

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=(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.
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Answer 1

To determine the parent function and the equation of the transformed function, we can analyze the transformations applied to the parent quadratic function \(y = x^2\).

1. **Identify the Parent Function**: The parent function for a parabola is given by:
\[
y = x^2
\]

2. **Determine Transformations**: The transformations typically include horizontal shifts, vertical shifts, reflections, or stretches. The options given suggest either a horizontal shift to the left or right.

- If the transformed function is in the form \(y = (x - k)^2\), it indicates a shift to the right by \(k\).
- If it is in the form \(y = (x + k)^2\), it indicates a shift to the left by \(k\).

3. **Evaluate Options**: Based on the provided response choices, the correct identification will depend on the specific transformation visible in the graph.

If the parabola shifts to the right by 2 units, it can be represented as:
\[
y = (x-2)^2
\]

If it shifts to the left by 2 units, it can be represented as:
\[
y = (x+2)^2
\]

### Answer Based on Provided Choices
Assuming we have looked at the graph, the correct matching would ideally indicate the transformation. Following the logic:

- If the parabola opens up in the normal direction (U-shaped) but appears shifted right or left based on the graph's visible properties, let’s summarize again:

**If it shifted right:**
- The parent function is \(y = x^2\)
- The equation of the transformed function is \(y = (x-2)^2\)

**If it shifted left:**
- The parent function is \(y = x^2\)
- The equation of the transformed function is \(y = (x+2)^2\)

### Conclusion
Considering your conclusions, the correct response should reflect the observed shift.

If the graph given shows a shift to the right by 2, then the answer is:
- The parent function is \(y = x^2\).
- The equation of the transformed function is \(y = (x - 2)^2\).

If it shows a shift to the left, then:
- The parent function is \(y = x^2\).
- The equation of the transformed function would be \(y = (x + 2)^2\).

You can select the answer based on what the graph illustrates regarding transformations.