Find g(x) when f(x)=x^2 is translated 9 units to the right. Write the result in vertex form a(x-h)^2+k with integer a, h, and k.
To translate a function horizontally by h units to the right, replace x with (x - h). Starting with f(x)=x^2 and translating 9 units right gives:
g(x)=f(x-9)=(x-9)^2.
In the form a(x - h)^2 + k, we have a = 1, h = 9, k = 0, so g(x)=1(x-9)^2+0 = (x-9)^2.
(If you want the expanded form: g(x)=x^2 - 18x + 81.)
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