Find the distance from point A (-1; 5) to the top of the parabola y = x ^ 2-4x + 5

First, we determine the coordinates of the vertex of the specified parabola: y = x² – 4x + 5.

We use the formulas:

x0 = -b / 2a = 4/2 • 1 = 2;

y0 = y (x0) = 2² – 4 • 2 + 5 = 4 – 8 + 5 = 1.

Thus, the parabola has its vertex at the point M (2; 1).

Find the distance between the points again using the appropriate formula:

d² = (x2 – x1) ² + (y2 – y1) ².

A (-1; 5) and M (2; 1).

d² = (2 – (-1)) ² + (1 – 5) ² = (2 + 1) ² + (-4) ² = 9 + 16 = 25.

Since d> 0, then d = √25 = 5.

Answer: 5.