Help 23,24 ​

23)

y=x^2 -8x +18

 

y -18 = x^2-8x

 

y-18 +16  = (x-8x+16)

 

y-2 = (x-4)^2

 

vertex(4,2)

 

Because (x-4)^2 has a coefficient of 1, and (y-k)= 1/4p(x-h)^2, p's value is 1/4.

 

Because x has a positive coefficient, the parabola is pointing upwards, so the focus is above the vertex. 

 

Focus(4, 2.25)

 

Directrix( y = 1.75)

 

24).

(x-2)^2 + (y-1)^2 = 16 

becomes 

(x-2+4)^2 + (y+1-6)^2 = 16

cleaned up 

(x+2)^2 + (y-5)^2 = 16