1. The problem asks to describe the transformation from the graph of $g(x) = x^2$ to $h(x) = -\left(\frac{x}{2}\right)^2$. 2. The original graph $g(x) = x^2$ is a parabola opening upwards. 3. The transformed graph $h(x) = -\left(\frac{x}{2}\right)^2$ involves two changes: - The negative sign in front reflects the graph over the x-axis, flipping it upside down. - The $\frac{x}{2}$ inside the square means the input $x$ is divided by 2, which stretches the graph horizontally by a factor of 2. 4. To confirm the horizontal stretch, recall that replacing $x$ by $\frac{x}{c}$ stretches the graph horizontally by a factor of $c$. 5. Therefore, the transformation is a reflection over the x-axis and a horizontal stretch. 6. Among the options given, the correct description is: "A reflection over the x-axis and a horizontal stretch."