Given a parabola with this equation:
$$y = x^2 + bx + c$$
And given 2 consecutive points of the parabola:
$$p_1 = (x_1, y_1), ~ p_2 = (x_2, y_2), ~x_2=x_1 + 1$$
Is there a way to find the vertex of the given parabola?:
$$v = (x_v, y_v) $$
PD: In the parabola equation, the only unknown is "b", and all variables (except the vertex) are given integers.
Update:
If the parabola equation is:
$$y = ax^2 + bx + c$$
and "a" is known. What changes in the solution?