Vertex of Quadratic Equation Calculator
This calculator helps you find the vertex of a quadratic equation in standard form $$ax² + bx + c$$. It’s useful for students, teachers, and engineers working with parabolas, as it instantly identifies the highest or lowest point on the graph. Just input the coefficients $$a$$, $$b$$, and $$c$$ to get the vertex in coordinate form.
Vertex of Quadratic Equation
Quadratic Vertex Formula
\[ x = \frac{-b}{2a}, \quad \] \[ y = \frac{-b^2 + 4ac}{4a} \]
To find the vertex of a quadratic equation in the form $$y = ax² + bx + c$$, use the vertex formula. The x-coordinate is calculated using $$-\frac{b}{2a}$$, and the corresponding y-value is obtained by substituting x back into the equation or using the simplified formula for y above.
The vertex of a quadratic function represents the turning point of its parabola. If $$a > 0$$, it’s the minimum point; if $$a < 0$$, it’s the maximum. This point is essential in graphing, optimization problems, and analyzing real-world quadratic models like projectile motion. For example, with the equation $$y = 2x² – 4x + 1$$, the vertex would be at $$x = 1$$, and $$y = -1$$, giving the vertex (1, -1).