The equation of a parabola is given.

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

What is the equation of the directrix of the parabola?

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