Question

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?
g(x) = (x – 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x – h)2 – 5
g(x) = (x – h)2 – 15

Answer 1

Y=(x-h)^2+k
a shift to the right by c units would be y=(x-h-c)^2+k
so 5 to the right
g(x)=(x+3-5)^2-10
g(x)=(x-2)^2-10
first option

Answer 2

The given function is:

f(x)= (x+3)² - 10

As we have to find g(x), which is 5 units right of f(x).

Now, first drawing the graph of f(x) on Desmos graphing,

The curve f(x) is a parabola having vertex (-3,-10).

As we know axis of symmetry is the line which divides the parabola in two parts , such that each of them are mirror images of each other.

Now , the curve g(x)= (x+3-5)² + K  →→→[∵ The axis of symmetry of g(x) is 5 units to the right of f(x)]

g(x) = (x-2)² + K,  →→→→→  -∞≤ k≤∞

When K= -10, g(x)=(x-2)² -10 , graph of f(x) and g(x) drawn below.

Option (A) , g(x) = (x-2)² + K,  →→→→→  -∞≤ k≤∞ is Right choice.