Question 1044839
(2x-3)^2=4x^2-12x+9. You expand this by squaring the first, twice the internal product, and squaring the second.
The x-component is -b/2a, where b is the x term coefficient and a is the square term coefficient, -(-12/8)=1.5.
The y-component is f(x), which is (3-3)^2=0
so (1.5,0) is the vertex.

{{{graph(300,300,-10,10,-10,10,(2x-3)^2)}}}