Parabola Calculator
Calculate the vertex, focus, directrix, and axis of symmetry of a parabola given its equation in standard form.
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isCalculator Editorial Team
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How to use this tool?
Follow these steps to use the Parabola Calculator:
- Enter coefficients for the standard form equation y = ax² + bx + c in the input fields labeled a, b, and c. Use any real number (e.g., 1, -2.5).
- Click "Calculate" or press Enter while in any input field.
- View results displayed in the right panel:
- Vertex (h, k) – the parabola's turning point.
- Focus and Directrix – used to define the parabola geometrically.
- Axis of Symmetry – vertical line through the vertex.
- Opening direction – upward (a > 0) or downward (a < 0).
- Note: Coefficient a must not be zero, or the equation is not a parabola. All inputs are unitless numbers.
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Frequently Asked Questions
A parabola is a U-shaped curve that can open upward or downward. It is defined by a quadratic equation y = ax² + bx + c.
The vertex (h, k) is found using h = -b/(2a) and k = c - b²/(4a).
The focus is a point inside the parabola, and the directrix is a line outside. For y = ax²+bx+c, focus is (h, k+1/(4a)) and directrix is y = k - 1/(4a).
