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

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

Explanation:

Answer 2

D. g(x) = (x+ 4)² + 6

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.