What is the rule for the vertex?

The axis of symmetry, which is the line that divides the parabola into two mirror images, also coincides with the x-coordinate of the vertex. Hence, the axis of symmetry is represented by the line x = -b/2a.

Alternatively, one can transform the standard form of the quadratic equation into vertex form by completing the square. This process involves manipulating the equation to express it as f(x) = a (x - h)2 + k, where (h, k) are the coordinates of the vertex.

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The parabola, represented by the quadratic equation f(x) = ax2 + bx + c, has a unique vertex that defines its shape. This vertex is a crucial point on the parabola, serving as a reference for understanding its overall characteristics.

The vertex's coordinates can be determined mathematically using the formula (-b/2a, f(-b/2a)). This formula helps locate the exact position of the vertex along the x-axis and the y-axis, respectively.