What Is FREE TOOLS Vertex Formula Calculator?
A Vertex Formula Calculator is a free online tool used to find the vertex of a quadratic equation or parabola. The vertex is the point where a parabola reaches its maximum or minimum value.
For a quadratic equation in standard form:
y = ax² + bx + c
the x-coordinate of the vertex is:
x = −b / 2a
After finding x, substitute it into the equation to find the y-coordinate.
How Does a Vertex Formula Calculator Work?
The calculator uses:
xᵥ = −b / 2a
Then:
yᵥ = a(xᵥ)² + bxᵥ + c
The vertex is written as:
(xᵥ, yᵥ)
Example
Given:
y = 2x² − 8x + 3
Here:
- a = 2
- b = −8
- c = 3
Find x:
xᵥ = −(−8) / (2 × 2) = 2
Now substitute x = 2:
y = 2(2²) − 8(2) + 3
y = 8 − 16 + 3 = −5
Therefore, the vertex is:
(2, −5)
What Can a FREE Vertex Formula Calculator Calculate?
A Vertex Formula Calculator can help you find:
- Vertex coordinates
- x-coordinate of the vertex
- y-coordinate of the vertex
- Maximum or minimum value
- Axis of symmetry
- Quadratic equation properties
- Vertex form of a parabola
The axis of symmetry is:
x = −b / 2a
Vertex Form
A quadratic equation can also be written in vertex form:
y = a(x − h)² + k
In this form, the vertex can be identified immediately:
Vertex = (h, k)
For example:
y = 3(x − 2)² + 5
has the vertex:
(2, 5)
Why Use a Vertex Formula Calculator?
A free calculator can help with:
- Algebra homework
- Quadratic equations
- Graphing parabolas
- Finding maximum and minimum values
- Checking mathematical work
- Understanding quadratic functions
In simple terms:
A FREE Vertex Formula Calculator quickly finds the turning point (vertex) of a parabola from a quadratic equation, helping you determine its maximum or minimum value and axis of symmetry.
