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
g(x) = (x – 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x – h)2 – 5
g(x) = (x – h)2 – 15
2 answers:
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.
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