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Which is the standard form of the equation of the parabola that has a vertex of (–4, –6) and a directrix of y = 3?

Guest Oct 16, 2018
 #1
avatar+91112 
+2

The directrix is  above the vertex, so this parabola turns downward

The form is

 

-4p [ y - k ] = [x - h]^2

 

(h, k)  is the vertex = (-4, -6 )     

 

And p is the distance between the vertex  and the directrix  given by 3 -  k  = 3 - (-6)  = 9

 

So we have

 

-4(9) [ y - (-6) ]  = [ x -  (-4) ] ^2

 

-36 [ y +  6]  = [ x + 4 ] ^2      divide both sides by -36

 

y  + 6  =  -(1/36) (x + 4)^2

 

y  = -(1/36) ( x + 4)^2  - 6

 

 

cool cool cool

CPhill  Oct 16, 2018

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