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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?

 

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asookles  May 16, 2018
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y  = 18x^2 + 4x  + 20

 

y = 18  (x^2  + 4/18x   +  20/18)   complete the square on x

 

y  = 18  ( x^2 + 4/18x + 16/1296 + 20 / 18  - 16/1296 )

 

y  = 18 [ ( x + 4/36)^2 +  89/81]

 

y = 18(x + 4/36)^2  + 178/9

 

(y - 178/9 )  = 18 ( x + 4/36)^2

 

(1/18) (y - 178/9)  = (x + 1/9)^2

 

The vertex  is  ( -1/9, 178/9 )

 

This parabola opens upward

 

We  have that     4p  = 1/18    ⇒ p   = 1/72

 

So....the focus is  at    ( -1/9, 178/9 + 1/72)  = (-1/9, 475/24 )

 

 

 

cool cool cool

 
CPhill  May 16, 2018

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