Question

What is the focus of a parabola with a standard form of y = 1/4x^2 - x - 1?

Include an explicit reasoning, just giving an answer won’t be helpful

Answer 1

(2, -1).

Explanation:

y = 1/4x^2 - x - 1

First convert to vertex form:

y = 1/4(x^2 - 4x) - 1

y = 1/4[(x - 2)^2 - 4] - 1

y = 1/4(x - 2)^2 - 2

The formula for the focus of the parabola y = a(x - h)^2 + k is (h, k+1/4a)

So here it is:

(2, -2+1/ 4*1/4)

= (2, -1).