Question

The equation of a parabola is given.

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

What is the equation of the directrix of the parabola?

Answer 1

Directrix equation: y = 11/2

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

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