放物線計算機

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はじめに

Parabola Calculator — Find the vertex, focus, and directrix of a parabola. Enter a, b, c to get an instant, accurate result.

計算式

For y = ax² + bx + c: vertex x = −b/(2a), vertex y = a(vertex x)² + b(vertex x) + c. With p = 1/(4a), the focus is at (vertex x, vertex y + p) and the directrix is the line y = vertex y − p.

ステップごとの説明

Enter the a.
Enter the b.
Enter the c.
Click Calculate to see your result instantly.

実例

Example: With a = 1, b = -4, c = 3, the Parabola Calculator gives Vertex X: 2, Vertex Y: -1, Focus Y: -0.75.

よくある質問

What if a = 0?

That's a straight line, not a parabola — a must be nonzero.

What are the focus and directrix used for?

Every point on the parabola is equidistant from the focus and the directrix line — they define the parabola's geometric shape.

What inputs does the Parabola Calculator need?

You'll need to provide: a, b, c. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Parabola Calculator?

The Parabola Calculator applies the formula exactly as calculated — For y = ax² + bx + c: vertex x = −b/(2a), vertex y = a(vertex x)² + b(vertex x) + c. With p = 1/(4a), the focus is at (vertex x, vertex y + p) and the directrix is the line y = vertex y − p. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Parabola Calculator free to use?

Yes, the Parabola Calculator is completely free, requires no signup, and runs instantly in your browser.