+0  
 
0
115
1
avatar+76 

The equation of a parabola is given.

 

y=−1/6x^2+7x−80

 

What is the equation of the directrix of the parabola?

Acceptfully  May 29, 2017
Sort: 

1+0 Answers

 #1
avatar+76925 
+2

y= (−1/6)x^2+7x−80      multiply both sides by -6

 

-6y  =    x^2   - 42x  +  480       subtract 480 from both sides

 

-6y  - 480   =  x^2  -  42x    take (1/2)  of 42  = 21.....square this  = 441  and add to both sides

 

-6y - 480 + 441  =   x^2  - 42x  +  441       simplify the left, factor the right

 

-6y - 39   =  (x  - 21)^2      factor the left side as

 

-6 (y  +  39/6)   =  ( x - 21)^2       (1)

 

Usiing the form

 

4p (y - k)  =  ( x  - h)      we  can   write (1)  as

 

4 (-3/2)(y - (-39/6) )   =  ( x  - 21)^2

 

 

The vertex  = ( x, k)  =  ( 21, -39/6)   and    p  = -3/2

 

And the directrix   is given by    y  = k - p  →   y  = -39/6 - (-3/2)  =  -39/6 + 3/2  = -39/6 + 9/6  =

-30/6  = - 5

 

See the graph, here :  https://www.desmos.com/calculator/hqmz4lhcvk

 

 

 

cool cool cool

CPhill  May 29, 2017
edited by CPhill  May 29, 2017

28 Online Users

avatar
avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details