1. The vertex of a parabola given by the quadratic function $y = ax^2 + bx + c$ is found using the formula for the x-coordinate of the vertex: $$x = -\frac{b}{2a}$$ 2. This formula comes from completing the square or using calculus to find the minimum or maximum point of the parabola. 3. Once you find the x-coordinate, substitute it back into the original quadratic equation to find the y-coordinate of the vertex. 4. For example, if the quadratic is $y = 2x^2 - 4x + 1$, then: $$x = -\frac{-4}{2 \times 2} = \frac{4}{4} = 1$$ 5. Substitute $x=1$ into the equation: $$y = 2(1)^2 - 4(1) + 1 = 2 - 4 + 1 = -1$$ 6. So the vertex is at the point $(1, -1)$. This method works for any quadratic function to find its vertex easily and accurately.