Quadratic Vertex X
Locate the x-coordinate of the vertex for any quadratic function y = ax² + bx + c. Enter the coefficients a and b to see where the parabola turns, whether it opens upward (minimum) or downward (maximum).
Double-check coefficient signs and decimal precision when using the result in engineering or physics applications.
Examples
- a = 1, b = 4 ⇒ vertex at x = -2
- a = 2, b = -8 ⇒ vertex at x = 2
- a = -0.5, b = 3 ⇒ vertex at x = 3
FAQ
What is the vertex of a quadratic?
The vertex is the single turning point of a parabola—its minimum if a > 0 or its maximum if a < 0.
Do I need the constant term c?
Not for the x-coordinate. The vertex's horizontal position only depends on a and b. You can compute y once you know x using the original equation.
What if a is zero?
If a = 0 the function is linear, not quadratic, and it has no vertex. Ensure you are working with a genuine quadratic expression.
How do I find the vertex's y-coordinate?
Plug the computed x into y = ax² + bx + c or use y = c - b²/(4a). Graphing calculators often report both values together.
How is this useful for graphing?
Knowing the vertex lets you sketch the axis of symmetry (x = -b / 2a) and quickly identify maximum or minimum values for optimisation problems.
Additional Information
- Vertex x-coordinate formula: x = -b / (2a).
- If a > 0 the parabola opens upward and the vertex is the minimum; if a < 0 it opens downward and the vertex is the maximum.
- The axis of symmetry passes through the vertex at x = -b / (2a).
- Use the vertex with two additional points to sketch an accurate parabola quickly.