Given the parabola g(x) = 5x^2 - 5x + 7.

We need to find the minimum value.

First, we need to find the first derivative.

==> g'(x) = 10x - 5

Now we will calculate the critical values which is the derivative zeros:

==> 10x - 5 = 0

==> 10x = 5

==> x = 1/2.

Since the sign of x^2 is positive, then we know that the function has a minimum value at x= 1/2

Then the function has a minimum value at x= 1/2

==> g(1/2) = 5(1/2)^2 - 5(1/2) + 7

                = 5/4 - 5/2 + 7

                 = ( 5 - 10 + 28)/4

                  = 23/4

Then, the minimum values is: f(1/2) = 23/4