what is the focus of y= x2- 2x- 3?

Question

I'm having difficulty finding it. PLEASE HELP

Answer 1

To find the focus of a parabola we need to put it in the form

y = a(x-h)²+k which has the vertex at (h,k) and focus at (h,k+1/(4a))

 

We have   y=x²-2x-3

Let's complete the square to get the proper format

take 1/2 of the coefficient of the x term (-2), square it, and add it to the problem..  (-1)² = 1

Don't forget, when we add 1 to the problem we must also subtract it back out...

y = x²-2x+1-3-1

y = (x-1)²-4

 

h=1, k=-4, a=1

Vertex at (1,-4)

Focus is (1,-4+1/4) = (1,-3 3/4) or (1,-15/4)