The focus is above the directrix 4 units (the difference between y=2 and y=6), so you know the parabola opens upward. The distance from either to the vertex is half that, or 2 units. If you call this distance p, the equation of the parabola with vertex (h, k) can be written as
... y = 1/(4p) × (x-h)² +k
In some parts of the world, this is the form referred to as "standard form." Filling in the numbers p = 2, (h, k) = (-5, 4), this is
... y = (1/8)(x +5)² +4
Elsewhere, "standard form" has this multiplied out.
... y = (1/8)x² + (5/4)x + 57/8
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Multiplying out (x+a)² gives x² +2ax +a².
