Parabola Calculator
MathCalculate the vertex, focus, and directrix of a parabola from its standard-form equation.
Vertex X
X-coordinate of the vertex.
Vertex Y
-5.1250
Y-coordinate of the vertex.
Focus Y
-5.0000
Y-coordinate of the focus (shares the vertex's X-coordinate).
Directrix Y
-5.2500
Y-coordinate of the horizontal directrix line.
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Creators
Odeh Ahwal0people find this calculator helpful
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Helpful
Saved
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Frequently Asked Questions
What input format does this use?
Standard form, y equals a times x squared plus b times x plus c, the most commonly used way to write a parabola's equation. Enter the three coefficients a, b, and c directly.
How is the vertex calculated from standard form?
The vertex x-coordinate is negative b divided by 2a. Substituting that back into the original equation, or using the shortcut c minus b squared over 4a, gives the vertex y-coordinate.
What are the focus and directrix?
Every point on a parabola is equally distant from a fixed point, the focus, and a fixed line, the directrix. They sit on opposite sides of the vertex, each offset by 1 divided by 4a from the vertex's y-coordinate for this upward or downward-opening form.
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