Find $$ g(x) $$, where $$ g(x) $$ is the translation 8 units right of $$ f(x)=x^{2} $$. Write your answer in the form $$ \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} $$, where $$ \mathrm{a}, \mathrm{h} $$, and k are integers. $$ g(x)= $$

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UpStudy AI · Accepted Answer

To translate the function $$ f(x) = x^2 $$ 8 units to the right, you adjust the input $$ x $$ by subtracting 8. This results in the new function:

$$
g(x) = (x - 8)^2
$$

Here, the function is expressed in the form $$ a(x - h)^2 + k $$ where:
- $$ a = 1 $$ (the coefficient of the squared term),
- $$ h = 8 $$ (the horizontal shift),
- $$ k = 0 $$ (no vertical shift).

**Final Answer:**
$$
g(x) = (x - 8)^2
$$
$$ g(x) = (x - 8)^2 $$

Find , where is the translation 8 units right of .
Write your answer in the form , where , and k are integers.

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Find , where is the translation 8 units right of . Write your answer in the form , where , and k are integers.