How is the vertex calculated in the intercept form of a parabola?

In the intercept form of a parabola, the equation is typically represented as ( y = a(x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the x-intercepts (roots) of the parabola. The vertex of the parabola lies exactly at the midpoint of these two intercepts.

To find the x-coordinate of the vertex, one averages the two roots ( r_1 ) and ( r_2 ). This average is calculated using the formula ( x = \frac{r_1 + r_2}{2} ). This computation gives the x-coordinate of the vertex because it represents the point that is equidistant from both intercepts, thereby locating the vertex precisely along the axis of symmetry of the parabola.

Thus, the correct method for calculating the vertex in this context is to use the average of ( r_1 ) and ( r_2 ).