Answer
Refer to the blue graph below.
Work Step by Step
RECALL:
(1) The graph of the function $y=f(x) + k$ involves a vertical shift of $|k|$ units (upward when $k$ is positive, downward when $k$ is negative) of the parent function $y=f(x)$.
(2) The graph of the function $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h$ is positive, to the left when $h$ is negative) of the parent function $y=f(x)$.
(3) The graph of the function $y=-f(x)$ involves a reflection across the x-axis of the parent function $y=f(x)$.
(4) The graph of the function $y=f(-x)$ involves a reflection across the y-axis of the parent function $y=f(x)$.
(5) The graph of the function $y=a\cdot f(x)$ involves either a vertical stretch of the parent function $y=f(x)$ when $a \gt 1$ or a vertical shrink when $0 \lt a\lt 1$.
(6) The graph of the function $y=f(ax)$ involves either a horizontal stretch of the parent function $y=f(x)$ when $0 \lt a \lt 1$ or a horizontal shrink when $a\gt 1$.
The parent function of the given function is $y=x^2$.
Graph this function. (Refer to the black graph below.)
The given function can be written as $f(x) = -[x-(-1)]^2+3$.
This equation is of the form $y=-f(x-h)+k$
Thus it involves the following graph transformations of the parent function $y=x^2$:
(1) with $h=-1$, there is a 1-unit shift to the left (refer to the orange graph below);
(2) a reflection across the x-axis (refer to the green graph below); and
(3) with $k=3$, there is a 3-unit shift upward (refer to the blue graph in the answer part above.
