p^2 - 2p - 3 = 0
p^2 - 2p = 3
halve the linear term (-2), square it and add it to both
sides
p^2 - 2p + 1 = 3 + 1
factor left, gather terms right
(p - 1)^2 = 4
(p - 1)^2 - 4 = 0
(1,-4) are the vector points of this parabola
You can factor to solve for p
(p + 1)(P - 3)
p = - 1
p = 3