Answer
see graph
Work Step by Step
The black graph is the graph of the standard function, $y=
x^2
$.
The red graph is the graph of the given function, $y=
3-\dfrac{1}{2}(x-1)^2
.$ It is the result of shifting the graph of the standard function by $1$ unit to the right, reflecting about the $y-$axis, and shifting $3$ units up.