College Algebra 7th Edition

RECALL: (1) The function $y=f(x-h)$ involves a horizontal shift of $h$ units to the right of the parent function $f(x)$ when $h\gt0$. The function involves a horizontal shift of $|h|$ units to the left when $h \lt0$. (2) The function $y=f(x)+c$ involves a vertical shift of $c$ units upward of the parent function $f(x)$ when $c \gt 0$. The function will involve a vertical shift of $|c|$ units downward when $c \lt 0$. The parent function of the given function is $y=x^2$. The given function can be written $y=f(x-3)+5$ where $f(x)$ is the parent function. Thus, the graph of the given function involves (i) a horizontal shift of $3$ units to the right and (2) a vertical shift of $5$ units upward of the parent function $y=x^2$. Therefore, to graph the given function: (1) Graph the parent function $y=x^2$ . (Refer to the red graph in the attached image below) (2) Shift the graph of the parent function 3 units to the right. (Refer to the orange graph in the attached image below.) (3) Shift the graph in Step (2) 5 units upward. (Refer to the blue graph in the attached image in the answer part above)