In vertex form:
y = x^2 +8x +16 -16 +18 ('completing the square)
y = (x+4)^2 +2 Vertex h, k = -4,2 Upward opening parabola (coefficient of (x+4)^2 is positive: +1 )
Re-arranging
y-2 = 4p (x+4)^2 4p = 1 p= 1/4 distance from vertex to directrix and focus
Directrix = y= 2- 1/4 = 1.75
Focus = y= 2+1/4 = 2 1/4 x = -4 so -4, 2 1/4
Graph:
y = x^2 + 8x + 18 complete the square on x
y = x^2 + 8x + 16 + 18 - 16
y = (x + 4)^2 + 2
(y - 2) = (x + 4)^2 (1)
In the form
4p (y - 2) = ( x + 4)^2 .....it's clear from (1) that p =1/4
This parbola turns upward
The vertex is (-4, 2)
The focus is given by : ( -4 , 2+ p) ⇒ (-4 , 2 + 1/4) ⇒ ( -4, 9/2)
The directrix is given by :
y = ( 2 - 1/4) = 7/4