Find the vertex, x intercept, and y intercept of the following equation: y = (x-3) ^2+5

The x-intercepts are: (3 + i√5, 0) and (3 - i√5, 0).

The y-intercept is (0,5).

The vertex is at (3, 5).

Step-by-step explanation:

The given equation y = (x-3) ^2+5 has the general form y = (x-h) ^2+k, whose vertex is at (h, k).

Thus, the vertex of y = (x-3) ^2+5 is (3,5).

Find the x-intercepts by setting y = (x-3) ^2+5 = 0 and solving for x. To do this, solve (x-3) ^2+5 = 0 for x. Subtracting 5 from both sides, we get:

(x-3) ^2 = - 5. We want to solve this for x.

Taking the square root of both sides, we get:

x-3 = √-1 * √5. Then x = 3 + i√5 and x = 3 - i√5. The x-intercepts are:

(3 + i√5, 0) and (3 - i√5, 0).