Question

What is the equation of the translated function, g(x), if
f(x) = x2?

A. g(x) = (x – 4)2 + 6
B. g(x) = (x + 6)2 – 4
C. g(x) = (x – 6)2 – 4
D. g(x) = (x + 4)2 + 6

Answer 1

Answer:

D.  g(x)  =  (x+ 4)² + 6

Step-by-step explanation:

Here, the given function is f(x)  = x²

Now,if a graph  x² is translated by (h,k) where:

h = Translation  done towards RIGHT

k = Translation  done towards UP

Then the translated equation is given as:

y =    (x-h)² + k    .... (1)

Now here, the graph is translated 6 UNITS UP and 4 UNITS LEFT.

⇒  h =  - 4 and k = 6

Substituting the value of h, k in (1) , we get:

g(x) =  (x-(-4))² + 6  =  (x+ 4)² + 6  

⇒ g(x)  =  (x+ 4)² + 6

Hence,  the equation of the translated function, g(x) is g(x)  =  (x+ 4)² + 6.

Answer 2

Answer:

d. g(x) = (x + 4)2 + 6

Step-by-step explanation: