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# Geomtry question

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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.

May 23, 2018
edited by lysxsa  May 23, 2018

### 2+0 Answers

#1
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idk how to delete this

May 23, 2018
edited by lysxsa  May 23, 2018
edited by lysxsa  May 23, 2018
#2
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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   May 24, 2018