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avatar+212 

The equation of a parabola is given.

 

y=−1/6x2+7x−80

 

What is the equation of the directrix of the parabola?

 

Enter your answer in the box.

lysxsa  May 23, 2018
edited by lysxsa  May 23, 2018
 #1
avatar+212 
0

idk how to delete this

lysxsa  May 23, 2018
edited by lysxsa  May 23, 2018
edited by lysxsa  May 23, 2018
 #2
avatar+87571 
+1

y = -(1/6)x^2  + 7x  - 80    factor out the  -1/6

 

y  = -(1/6)  [ x^2  - 42x + 480 ]      complete the square  on  x

 

y = -(1/6)  [ x^2 - 42x + 441 + 480 - 441 ]

 

y  = -(1/6)  [  ( x - 21)^2 + 39 ]

 

y = (-1/6)(x - 21)^2   - 39/6

 

 (y +39/6) = (-1/6) (x - 21)^2     multiply both sides by -6

 

-6(y  + 39/6)  = ( x - 21)^2

 

-6 ( y + 6.5)  = (x - 21)^2

 

4p  = -6

p = -6/4  = -3/2

 

The vertex is  ( 21, -6.5)

 

The directrix is given by :  y   = -6.5  - p  =  -6.5  - (-3/2)  = -5

 

 

cool cool cool

CPhill  May 24, 2018

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