What is the equation for a 3-dimensional parabola (paraboloid) opening up toward the positive z-axis with a vertex on the xy-plane at the point (3, 1)?

The equation for a 3-dimensional paraboloid that opens upwards toward the positive z-axis and has its vertex at the point (3, 1) can be expressed as:

z = a((x – 3)² + (y – 1)²)

In this equation:

• z represents the height (or depth) above the xy-plane.
• (x – 3) and (y – 1) represent the deviation of the points (x, y) from the vertex point (3, 1).
• a is a positive constant that determines how