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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=(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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1 answer

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 \(k\).
  1. 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.