Question 1 of 10 How would you describe the difference between the graphs of \( f(x)=2 x^{2} \) and \( g(x)=-2 x^{2} \) ? A. \( g(x) \) is a reflection of \( f(x) \) over the \( y \)-axis. B. \( g(x) \) is a reflection of \( f(x) \) over the line \( y=-1 \). C. \( g(x) \) is a reflection of \( f(x) \) over the x-axis. D. \( g(x) \) is a reflection of \( f(x) \) over the line \( y=x \).

The graphs of \( f(x) = 2x^2 \) and \( g(x) = -2x^2 \) offer a fantastic illustration of symmetry! The function \( f(x) \) opens upwards, resembling a smiling face, while \( g(x) \) flips it upside down, creating a frown. They are equal in width but opposite in direction, showing how a negative sign transforms the shape instantly. When you take a closer look at their equations, you can find that \( g(x) \) is indeed just a reflection of \( f(x) \) over the x-axis. This realization reveals the beauty of quadratic functions and how transformations can alter their appearances, giving you another reason to love the world of graphs!