How would you find the minimum point on a quadratic graph?

Please see the following:

To find the minimum of a quadratic graph is only relevant where a>0, i.e y = ax^2 + bx + c, where a>0. In this case, this can be solved by finding where the gradient is 0. The gradient is found by differentiation as follows:

dy/dx = 2ax + b

If we set the gradient to 0, we see 2ax+b=0 and therefore x=-b/(2a) at the minimum point of the quadratic graph.