Question

The equation of a parabola is given.

y = ½x² + 6x + 24

What is the equation of the directrix of the parabola?

Enter your answer in the box.

_________

Answer 1

Answer: y = 5.5

Just comfirm that the answer above is correct :)

Answer 2

The equation of the directrix of the parabola is
`y=5.5`

Explanation:

we know that

The equation of a vertical parabola in standard form is equal to

`(x-h)^(2)=4a(y-k)`

where

(h,k) is the vertex of the parabola

y=k-a is the directrix of the parabola

In this problem we have

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

Convert to standard form

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

`y-24=(1)/(2)(x^(2)+12x)`

`y-24+18=(1)/(2)(x^(2)+12x+36)`

`y-6=(1)/(2)(x^(2)+12x+36)`

`y-6=(1)/(2)(x+6)^(2)`

therefore

`(x+6)^(2)=2(y-6)` ----> standard form

The vertex is the point (-6,6)

`4a=2`

`a=(1)/(2)=0.5`

The directrix of the parabola is

`y=k-a`

`y=6-0.5=5.5`

therefore

The equation of the directrix of the parabola is
`y=5.5`