What are the vertex ,focus, and directrix of the parabola with the equation y = x2 - 6x + 15?

Select one:
a. Vertex: (3, 6), Focus: (3, 6.25), Directrix: y = 5.75
b. Vertex: (3, 6), Focus: (3, 5.75), Directrix: y = 6.25
c. Vertex: (6, 3), Focus: (6, 3.25), Directrix: y = 2.75
d. Vertex: (3, -6), Focus: (3.25, -6), Directrix: y = 2.75

Question

What are the vertex ,focus, and directrix of the parabola with the equation y = x2 - 6x + 15?

Select one:
a. Vertex: (3, 6), Focus: (3, 6.25), Directrix: y = 5.75
b. Vertex: (3, 6), Focus: (3, 5.75), Directrix: y = 6.25
c. Vertex: (6, 3), Focus: (6, 3.25), Directrix: y = 2.75
d. Vertex: (3, -6), Focus: (3.25, -6), Directrix: y = 2.75

1645323 · Answer

@MathLegend @MathGeekinProgress

mathmale · Answer

Your best bet is to determine the vertex of the given parabola.
To do this, you might want to "complete the square."  
If you're not familiar with this, ask for help.

Once you have the vertex, you need to locate the focus.  The distance between focus and vertex is called ' p '      This shows up in the following equation for a VERTICAL parabola:

$$4p(y-k)=(x-h)^2$$