How is the vertex of a parabola found in standard form?

To determine the vertex of a parabola in standard form represented as ( y = ax^2 + bx + c ), the x-coordinate of the vertex can be found using the formula ( x = -\frac{b}{2a} ). This formula derives from the properties of quadratic functions and tells us the x-value where the parabola reaches its maximum or minimum, depending on the direction it opens (upwards for ( a > 0 ) or downwards for ( a < 0 )).

Once the x-coordinate is calculated, the y-coordinate can be further computed by substituting this x-value back into the original quadratic equation, but the essential step to locate the vertex's x-coordinate is through the use of the formula ( x = -\frac{b}{2a} ). This makes the choice that focuses on this formula the correct one because it encapsulates the essential calculation needed to find the vertex's position along the x-axis, which is crucial for any analysis of the parabola's graph.

In contrast, calculating ( y = f\left(-\frac{b}{2a}\right) ) simply gives the y-coordinate of the vertex after the x-coordinate has been determined, and thus