What are the vertex, focus, and directrix of the parabola with equation y = x^2 – 10x + 33?

Opens up so
(x-h)^2=4P(y-k)
complete the square with the x term
take 1/2 of -10 and square it and add that to both sides

y+25=x^2-10x+25+33
factor perfect square
y+25=(x-5)^2+33
minus 33 both sides
y-8=(x-5)^2
force factor out a 4
4(1/4)(y-8)=(x-5)^2
(x-5)^2=4(1/4)(y-8)
vertex is (5,8)

distance from directix is P or 1/4 or 0.25
since opens up, directix is ycoordinate-0.25 aka y=7.75 is directix
focus=(5,8+0.25)=(5,8.25)

vertex=(5,8)
directix: y=7.75
focus: (5,8.25)