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# mATH

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11. The equation of a parabola is given y=1/2x^2+6x+24.

What is the equation of the directrix of the parabola?

12. The equation of the parabola is (y-1)^2=16(x+3).

What is the equation of the directrix of the parabola?

May 3, 2017

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11. The equation of a parabola is given y=1/2x^2+6x+24.

What is the equation of the directrix of the parabola?

First.....find the vertex.....complete the square on x and y

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

y = (1/2) [ (x + 6)^2 - 12  ]

y = (1/2) (x + 6)^2  - 6      the vertex is ( -6, - 6)    ....add 6 to both sides

(y + 6)  =  (1/2) (x + 6)^2      multiply both sides by 2

2(y + 6)  = ( x + 6)^2

And in the form   4p (y - k)  = (x + 6)^2

4p  = 2

p = 1/2

So......the equation of the directrix  is y = -6.5

12. The equation of the parabola is (y-1)^2=16(x+3).

What is the equation of the directrix of the parabola?

The vertex  is ( -3, 1)    and the parabola opens to the right

The form is

(y - k)^2  = 4p(x + 3)

So    4p  = 16   →  p  = 4

And the equation of the directrix  is    x  =   -7

May 3, 2017