Answer
see graph
Work Step by Step
The black graph is the graph of $
f(x)=x^2$.
The red graph is the graph of the given function, $
f(x)=-(x-4)^2+\dfrac{3}{2}
.$ It is the result of shifting the points of the black graph $4$ units to the right, reflecting about the $x-$axis, and shifting $\dfrac{3}{2}$ units up.