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.