First, you need to find the vertex. This is where the minimum or maximum value will be found. The x value for the vertex can be found by calculating -b / 2a. In this case, it is -24 / 2(4) = -24/8, or -3. The y value can be found by plugging this value into the original equation that is -28. So, the vertex is (-3, -28) so the min or max is -28.
If a is positive, the vertex is a minimum. If a is negative, the vertex is a maximum. Therefore, -28 is the minimum of this equation.