Question

the graph of g(x) is a translation of the function f(x) = x2. the vertex of g(x) is located 5 units above and 7 units to the right of the vertex of f(x). which equation represents g(x)? g(x) = (x 7)2 5 g(x) = (x – 7)2 5 g(x) = (x 5)2 7 g(x) = (x – 5)2 7

Answer 1

Translation of 7 units to the right ⇒ subtract 7 units to the argument ⇒ f(x-7)

Translation of 5 units up ⇒ add 5 units to the function ⇒ f(x) + 5

g(x) = f (x-7) + 5 = (x-7)^2 + 5

The subtraction of 7 units to the argument of the function (this is x) translates the function 7 units to the right.

Adding 5 units to the function f, translates the graph 5 units up.