MATH CALCULATOR
Parabola Calculator
Calculate parabola properties and equations easily with our online calculator.
What is the Parabola Calculator & How does it work?
A parabola is a U-shaped curve that can be described by the equation ( y = ax^2 + bx + c ). The vertex of the parabola, which is its highest or lowest point, can be found using the formula ( x = -frac{b}{2a} ). This calculator helps you determine the vertex and other properties of a parabola given its coefficients.
The focus of a parabola is a fixed point inside the curve, and the directrix is a line perpendicular to the axis of symmetry. For a parabola in the form ( y = ax^2 + bx + c ), the focus can be calculated using the formula ( (h, k + frac{1}{4a}) ) where ( h ) and ( k ) are the coordinates of the vertex.
y = ax^2 + bx + c
a = coefficient of x2, b = coefficient of x, c = constant term
Parameters
Result—
Frequently Asked Questions
How do I find the vertex of a parabola?
Use the formula x = -b / (2a) to find the x-coordinate of the vertex, then substitute it back into the equation y = ax^2 + bx + c to get the y-coordinate.
What is the focus of a parabola?
The focus of a parabola in the form y = ax^2 + bx + c is located at (h, k + 1/(4a)), where (h, k) is the vertex.
How do I determine the directrix of a parabola?
The directrix of a parabola in the form y = ax^2 + bx + c is the line y = k - 1/(4a), where (h, k) is the vertex.
Can this calculator handle any type of parabola?
Yes, it can handle parabolas in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
What if I only know two points on the parabola?
You would need to use those points to set up a system of equations based on y = ax^2 + bx + c and solve for a, b, and c.
How do I graph a parabola using this calculator?
Input the coefficients a, b, and c into the calculator to find the vertex, focus, and directrix. Use these points to plot the parabola on a coordinate plane.
Is there a maximum or minimum value for a parabola?
If a > 0, the parabola opens upwards and has a minimum value at its vertex. If a < 0, it opens downwards with a maximum value at the vertex.
Results are for informational purposes only and do not constitute professional advice.