Question

What is the vertex and p-value of this parabola?

Answer 1

• vertex: (-7, 5)
• p = 2

Explanation:

The vertex is halfway between the focus and the directrix:

((-7, 7) +(-7, 3))/2 = (-14, 10)/2 = (-7, 5) . . . . vertex coordinates

The value of p is the distance from the focus to the vertex:

7 -5 = 2 = p

In vertex form, the equation of the parabola is ...

y = 1/(4p)(x -h)^2 +k . . . . . . vertex (h, k)

y = 1/8(x +7)^2 +5