b. \( y=2 x^{2}-2 \)

The equation \( y=2 x^{2}-2 \) describes a parabola that opens upwards, with its vertex at the point (0, -2). This means that the lowest point on the graph is at y = -2 when x is 0. The "2" in front of the \( x^{2} \) serves as a scaling factor, making the parabola narrower than the standard \( x^{2} \) graph. In the real world, parabolas can model various phenomena such as the trajectory of projectiles or the shape of satellite dishes. When you throw a ball, for example, its path can be approximated by quadratic equations like this one – showcasing the amazing connection between mathematics and our daily experiences!