Let x be number of T-Shirts made.
Therefore,
Revenues from the sell = 12*x = 12x
The cost making them = 20+(8*x) = 20+8x
Profits = 12x-(20+8x) = 12x -20-8x = 4x - 20
Now, this profit should be atleast $100. Then,
100<4x-20 => 100+20<4x => 120<4x => 120/4<x => x>30
Therefore, more than 30 T-shirts should be made in order to make atlease $100 profit.
The general vertex form equation of the parabola is

The Axis of Symmetry is given by
x=h
For the given equation the Equation of the Axis of symmetry for the parabola y=1/2(x-3)^2+5 as x=3.
You have to distribute the minus sign to the second parenthesis, changing the sign of every term:

4x-5y=3
4x-5(10)=3
4x-50=3
+50 +50
4x=53
/4 /4
x=53/4