Question

The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function
Graph is an upward u shape with points (-2,0),(-3,2),(-1,2)
Parent function is y= x^2 transformed function is y =(x-2)^2
y= (x-2)^2, y = x^2
y= x^2 , y=(x+2)^2
y= (x+2)^2, y= x^2

Answer 1

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.

1. 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**