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foci y=x^2+x+1

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foci y=x²+x+1

Solution

(−12 , 1)

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Parabola Focus

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(y−k)=(x−h)² is the standard equation for an up-down facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite y=x²+x+1 in the standard form

4· 14 (y−34 )=(x−(−12 ))²

(h, k)=(−12 , 34 ), p=14

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (−12 , 34 ) along the y-axis

(−12 , 34 +p)

=(−12 , 34 +14 )

Refine

(−12 , 1)

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+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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foci y=x^2+x+1

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foci y=x^2+x+1

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