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We are given two graphs:

1. The first graph is of the function \( f(x) = x^2 \), a standard parabola with vertex at the origin (0, 0) and symmetry around the y-axis.
   
2. The second graph is of the function \( g(x) \), which is described as a linear transformation of \( f(x) \). The graph looks like it has been reflected and scaled.

From observation, the second graph appears to be reflected across the x-axis and vertically stretched. The general form for a linear transformation of a quadratic function \( f(x) \) is:
\[
g(x) = a f(x) + b
\]
For reflections and vertical scaling, we typically have the form \( g(x) = -a f(x) \). Here, \( f(x) = x^2 \), so:
\[
g(x) = -a x^2
\]
Looking at the graph, the vertex is still at \( (0, 0) \), so there is no vertical shift. The graph opens downward, indicating that \( a \) is negative.

From the stretch, it appears that \( a = 1 \), so:
\[
g(x) = -x^2
\]

Thus, the equation of the second graph is \( g(x) = -x^2 \).

Would you like more details or have any questions? Here are 5 related questions to explore:

1. How does the coefficient \( a \) in \( g(x) = a f(x) \) affect the graph?
2. What is the effect of reflecting a graph over the x-axis?
3. How do you recognize vertical shifts and stretches in a graph?
4. What are the general steps to find a transformation equation from a graph?
5. What other types of transformations could apply to quadratic functions?

**Tip:** When identifying transformations, always check for reflections, stretches, shifts, and dilations by comparing key points like the vertex and intercepts.

The graph of the function f(x) = x^2 is given below. Below is a graph of g(x), a linear transformation of f. What is the expression for g(x)?

Solve the linear transformation of the quadratic function f(x) = x^2. The graph shows a reflection and a stretch, leading to the equation g(x) = -x^2. Learn how to interpret graph transformations and write the transformed function.

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