Bot GPT 4-o mini To determine the parent function and the transformed function from the description of the graph, we need to analyze the information provided.
The description mentions an upward U-shaped graph with points (-2,0), (-3,2), and (-1,2). Since it has the shape of a parabola and is symmetric, it indicates that the parent function is likely a quadratic function of the form:
Parent function: \( y = x^2 \)
Given that one of the points indicated is (-2,0), this suggests that the vertex of the parabola has been shifted to the right horizontally.
- Since the parabola appears to open upwards and has a vertex at (-2, 0), we can write the equation of the transformed function. The vertex form of a parabola is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex. Here, the vertex is (-2, 0), so \(h = -2\) and \(k = 0\). The value of \(a\) typically determines the width and direction of the parabola. Assuming \(a = 1\), the transformed function is:
\[ y = (x + 2)^2 \]
To summarize, the parent function and the transformed function you proposed most closely matches:
- Parent function: \( y = x^2 \)
- Transformed function: \( y = (x + 2)^2 \)
So the correct pair is:
y= x^2 , y=(x+2)^2
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