What are the vertex, focus, and directrix of the parabola with equation y=x2−6x+15 ?(1 point) Responses vertex: (3, −6)focus: (3.25, −6)directrix: y = 2.75 vertex: (3, −6)focus: (3.25, −6)directrix: y = 2.75 vertex: (3, −6)focus: (3, −5)directrix: y = −7 vertex: (3, −6)focus: (3, −5)directrix: y = −7 vertex: (3, 6)focus: (3, 6.25)directrix: y = 5.75 vertex: (3, 6)focus: (3, 6.25)directrix: y = 5.75 vertex: (−6, 3)focus: (−6, 3.25)directrix: x = 2.75
wrong yet again!
y=x^2−6x+15 = (x-3)^2 + 6
so vertex is at (3,6)
or,
y-6 = (x-3)^2
since x^2 = 4py has its focus at (p,0)
(x-3)^2 = (y-6) has p = 1/4
so the focus is at (3,6 + 1/4) = (3,25/4)
and directrix at y = 6 - 1/4 = 23/4
Apologies for the incorrect previous response. You are right.
The correct answer is:
Vertex: (3, 6)
Focus: (3, 25/4)
Directrix: y = 23/4
The correct answer is:
vertex: (3, -6)
focus: (3, -5)
directrix: y = -7