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# The equation of a parabola is given. y=−16x^2+7x−80

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The equation of a parabola is given. y=−16x^2+7x−80

What is the equation of the directrix of the parabola?

Kakarot_15  May 2, 2017
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y=−16x^2+7x−80     factor  out -16

y  =  -16 (x^2  - 7/16 x + 5)   complete the square on x

y  =  -16 (  x^2   - 7/16 x  + 49/1024  +  5   -  49/1024 )

y  =  -16 [  (x - 7/32)^2  + 5071/1024 ]

y =  -16(x - 7/32)^2  - 5071/64

The vertex is   ( 7/32, -5071/64)

To find the focus....solve this......    1/4p  = -16   → p  = -4

So.....the focus is ( 7/32, -5327/64)

And the equation of the directrix  is      y  =  -5071/64  +  4  = -4815/64

Here's a graph  :  https://www.desmos.com/calculator/nhy4nlep4o

CPhill  May 2, 2017

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