Use the graph of $f(x)=|x|^{2}$ to graph $g(x)=-|x+2|+3$. Describe each transformatoin and the order of transformations.

Step 1 ：First, identify the base function and the transformations. The base function is \(f(x) = |x|^2\) and the given function is \(g(x) = -|x+2|+3\).

Step 2 ：The first transformation is a horizontal shift to the left by 2 units. This is represented by the \(x+2\) inside the absolute value function. So, the intermediate function is \(h(x) = |-x|^2\).

Step 3 ：The second transformation is a reflection across the x-axis. This is represented by the negative sign in front of the absolute value function. So, the intermediate function is \(i(x) = -|-x|^2\).

Step 4 ：The third transformation is a vertical shift up by 3 units. This is represented by the \(+3\) outside the absolute value function. So, the final function is \(g(x) = -|-x|^2 + 3\).

Step 5 ：Now, graph the base function \(f(x) = |x|^2\) and apply the transformations in the order described above.

Step 6 ：First, shift the graph of \(f(x) = |x|^2\) to the left by 2 units to get the graph of \(h(x) = |-x|^2\).

Step 7 ：Next, reflect the graph of \(h(x) = |-x|^2\) across the x-axis to get the graph of \(i(x) = -|-x|^2\).

Step 8 ：Finally, shift the graph of \(i(x) = -|-x|^2\) up by 3 units to get the graph of \(g(x) = -|-x|^2 + 3\).

Step 9 ：The graph of \(g(x) = -|-x|^2 + 3\) is the result of these transformations applied to the base function \(f(x) = |x|^2\).