The graph of the function f(x) = ax^2 + bx + c (where a, b, and c are real and non zero) has two x- intercepts. explain how to find the other x-intercept if one x-intercept is at ( -b/2a + 3,0)

The vertex of the parabola is given by :

                          .

So, is the first coordinate of the vertex, which means it is also the point where the line of symmetry passes.

The line of symmetry divides the parabola into 2 symmetrical parts: the x-intercepts are also symmetrical to each other with respect to this line.

So, if one of the x-intercepts is , that is 3 units to the right of the x-intercept, the other must be 3 units to the left. Thus, the second x-intercept is :

,

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