Question

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)

Answer 1

The vertex of the parabola is given by :

                          $\displaystyle{ ( \frac{-b}{2a}, f(\frac{-b}{2a}) )$.

So, $\displaystyle{ \frac{-b}{2a}$ 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 $\displaystyle{ (\frac{-b}{2a}+3, 0)$, 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 :

Answer: $\displaystyle{ (\frac{-b}{2a}-3, 0)$,