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 What is the equation of the directrix of this parabola?

 

y = -5/8x^2 -3x + 4

whosmans  Mar 28, 2018
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y  =   (-5/8)x^2 - 3x  + 4

 

y  - 4   =  (-5/8)x^2  - 3x       complete the square on the right

 

y  - 4  =  (-5/8)  [ x^2  +  24/5x + 576/100  -  576/100]

 

y  - 4  =  (-5/8) [ x + 24/10]^2  + 18/5

 

y - 4  -  18/5  =  (-5/8)[x + 24/10]^2

 

(y  - 38/5)  = (-5/8)[ x + 24/10]^2     multiply both sides by -8/5

 

(-8/5) (y - 38/5)  = ( x + 24/10)^2

 

The vertex is (   -24/10, 38/5)  =    ( -12/5, 38/5)

 

Using the form

 

4p (y - k)  =  (x - h)^2

 

4p   =  -8/5

p  = -2/5

 

This parabola  turns downward so the equation of the directrix  is

 

y  = 

 

38/5 - p    

 

38/5 -  (-2/5)   =   

 

8

 

So    y  =  8 

 

 

cool cool cool

CPhill  Mar 28, 2018

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