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The equation of a parabola is given.

 

y=18x2+4x+20

 

What are the coordinates of the focus of the parabola?

 

Enter your answer in the boxes.

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 Apr 15, 2019
 #1
avatar+107011 
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y = 18x^2 - 4x + 20

 

y - 20  = 18 [ x^2 - 2/9 x  +1/81 - 1/81 ]

 

y - 20  =  18 ( x - 1/9)^2   - 2/9

 

y - 180/9 + 2/9  =  18 (x - 1/9)^2

 

(y - 178/9)  = 18(x - 1/9)^2

 

(1/18)(y - 178/9) = ( x - 1/9)^2

 

The vertex is  (1/9, 178/9)

 

4a = 1/18

a = 1/72

 

The focus is  ( 1/9, 178/9 + 1/72)  =   (1/9, 475/24)

 

 

 

cool cool cool

 Apr 15, 2019

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