#1**0 **

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:

ElectricPavlov Mar 12, 2018

#2**+1 **

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

CPhill Mar 12, 2018