Final answer:
To find the minimum distance between two parabolas x - y² = 0 at (0,3), graph the parabolas, find the corresponding points with the same x-coordinate on each parabola, calculate the distance between those points, and find the minimum distance.
Step-by-step explanation:
To find the minimum distance between parabolas x - y² = 0 at (0,3), we can start by graphing the two parabolas on a coordinate plane. The equation x - y² = 0 can be rewritten as y = ±√x. By substituting different x-values into this equation, we can find the corresponding y-values for each parabola. Then, we can calculate the distance between the two points on each parabola that have the same x-coordinate. Finally, we compare all these distances to find the minimum distance.