Question

State the various transformations applied to the base function f(x) = x^2 to obtain a graph of the function g(x) = (x - 3)^2 + 5

(A) Horizontal shift of 3 units to the right and a vertical shift upward of 5 units.
(B) Horizontal shift of 5 units to the right and a vertical shift downward of 3 units.
(C) Horizontal shift of 3 units to the left and a vertical shift upward of 5 units.
(D) Horizontal shift of 5 units to the left and a vertical shift upward of 3 units.

So far all I'm confident of is that B is NOT the answer because +5 would indicate an upward shift.
Leaning towards C because of the base function's x^2 would cancel out the ^2 in the second function, leaving the -3 to create a negative shift to the left.

Answer 1

f(x-k) shifts the graph of f(x) to RIGHT by k units

Answer 2

So would that make A be the answer?

Answer 3

graph them here and see
https://www.desmos.com/calculator

Answer 4

its not loading for me

Answer 5

its okay, A is right

Answer 6

thank you so much

Answer 7

yw!