Your new flashlight uses a parabolic mirror which can be modeled by the equation (x – 2)² = 5(y + 1), where x and y are measured in centimeters. you need to place a new light bulb in your flashlight. how far away from the vertex of the parabolic mirror should you place the bulb to ensure a perfect beam of light?

The given equation is
(x - 2)² = 5(y + 1).

The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5,    so that  p = 5/4
k = -1

The vertex is at 
(h,k) or (2, -1)

The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)

We should place the bulb at p = 5/4 from the vertex.

1 1/4 or 1.25 cm