For a quadratic in standard form (y = ax^2 + bx + c), find the x-coordinate of the vertex using (x = -frac{b}{2a})
Substitute (x = -frac{b}{2a}) into the quadratic equation to find the y-coordinate
The vertex is (left(-frac{b}{2a}, fleft(-frac{b}{2a}right)right))
For a quadratic in vertex form (y = a(x-h)^2 + k), the vertex is ((h, k))
If the equation is factored, expand it or use the axis of symmetry to find the vertex
The axis of symmetry is (x = -frac{b}{2a}) for standard form
The vertex lies on the axis of symmetry
If needed, complete the square to rewrite the quadratic in vertex form