+19 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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+129850 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 )
