If you don't know where Galactus got his -b/(2a) expression, you may understand this:

The max value of your parabola is the x-coordinate of the vertex.

The x-coordinate of the vertex is the midpoint of the x-intercepts.

You found the x-intercepts to be -.5 and 2.5.

Using the midpoint formula: (-.5 + 2.5)/2 = 1

So, 1 is the x-coordinate of the vertex and the max value of the parabola.

BTW, if you want to derive the -b/(2a) expression, you'd have to add the two parts of the quadratic formula together and divide by 2. It's much simpler to memorize -b/(2a).