Question

The equation of a parabola is given.

Answer 1

Answer:

Directrix equation:  y = 11/2

y = k - c = 6 - 1/2 = 11/2

Step-by-step explanation:

y=(1/2) x^2+6x+24

factor this

y =  (1/2)* [  x^2  + 12x  ]  +  24

y =  (1/2)* [  x^2  + 12x  + 36  -  36]  +  24

y =  (1/2)* [  (x + 6)^2  -  36]  +  24

y =  (1/2)*   (x + 6)^2  - 18 +  24

y =  (1/2)*   (x + 6)^2  + 6

y - 6 =  (1/2)*   (x + 6)^2

2*(y - 6)  =   (x + 6)^2

4c = 2,   (h, k) = (-6, 6)

c = 1/2

Directrix equation:  y = k - c = 6 - 1/2 = 11/2