Parabola Properties Calculator
Parabola Properties with explicit inputs, formulas and domain checks.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Vertical-axis parabola in Cartesian coordinates; no rotated conics.
Example Calculation
- a in y=ax²+bx+c: 1
- b: -4
- c: 3
y=x²−4x+3 has vertex(2,−1), focus(2,−0.75), directrix y=−1.25.
Frequently asked questions
How do I use this calculator?
Enter a in y=ax²+bx+c, b, c. The result updates automatically. Use Reset to restore the example values.
What method does it use?
h=−b/(2a); k=c−b²/(4a); p=1/(4a); focus=(h,k+p); directrix y=k−p.. Vertical-axis parabola in Cartesian coordinates; no rotated conics.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.