Problem

A parabola has focus \((0,~2)\) and directrix \(y~=~-2\). Locate the vertex midway between them, compare the focus position with the vertex, and state the opening direction with justification.

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What this problem is really about

Opening direction depends on where the focus lies relative to the vertex, not on the directrix orientation alone. We’ll use the line’s perpendicular direction for the axis, locate the midpoint vertex, compare the focus position with it, apply the toward-focus rule, and confirm with signed p and standard form.

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It opens right because the focus is 2 units from the y-axis, so the parabola points horizontally.

It opens up because the directrix is below the focus, so the vertex is between them and the parabola opens toward the focus.

It opens down because the directrix is below the focus, so the parabola must open away from the focus.

It opens down because the directrix y = -2 is a horizontal line, and horizontal directrices always make parabolas open downward.

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A parabola has focus \((0,~2)\) and directrix \(y~=~-2\). Locate the vertex midway between them, compare the focus position with the vertex, and state the opening direction with justification.

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