To determine the parent function and the equation of the transformed function based on the graph, we need to identify the form of the transformation.
The parent function for a quadratic is generally given by the equation \(y = x^2\). If the graph shows a transformation, such as a horizontal shift to the left or right, it would be represented in the function as \(y = (x - h)^2\), where \(h\) indicates the horizontal shift.
Based on the typical transformations:
- A leftward shift would be expressed as \(y = (x + k)^2\) for some \(k\).
- A rightward shift would be expressed as \(y = (x - k)^2\).
If the function has been shifted left by 2 units, the equation would be \(y = (x + 2)^2\). If it has been shifted right by 2 units, it would be \(y = (x - 2)^2\).
Since the question mentions the options regarding the transformed function being in the form of \((x + 2)\) or \((x - 2)\), the correct choice will depend on the observed shift in the graph you referred to.
Given the choice options, it seems clear that:
- The parent function is \(y = x^2\).
- If the graph represents a leftward shift by 2, then the transformed function is \(y = (x + 2)^2\).
- If the graph represents a rightward shift by 2, then the transformed function is \(y = (x - 2)^2\).
From the responses provided:
- If the graph shows a left shift, the correct option is: The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x + 2)^2\).
- If the graph shows a right shift, then the correct option is: The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x - 2)^2\).
Please confirm the direction of the shift based on the graph to select the correct response!
3 answers