What type of curve is mirror-symmetrical and typically U-shaped?

The type of curve that is mirror-symmetrical and typically U-shaped is a parabola. Parabolas are defined as the set of all points that are equidistant from a fixed point known as the focus and a straight line called the directrix. This geometric property leads to their characteristic U shape, making them symmetrical about a vertical line (the axis of symmetry).

In addition to their symmetry and shape, parabolas have numerous applications in physics and engineering, particularly in projectile motion and the design of reflective surfaces like satellite dishes and parabolic microphones. The unique properties of their symmetry also contribute to their usefulness in modeling certain types of real-world scenarios.

The other options, while they have their own unique characteristics, do not fit the description provided. For instance, an ellipse is elongated and circularly symmetric rather than U-shaped, a hyperbola consists of two separate curves (not mirror-symmetrical about a single axis), and a circle is symmetric in two dimensions but does not exhibit the U-shaped characteristic.