4) Find g(x) , where g(x) is the translation 3 units down of f(x)=x^2 4) Write your answer in the form a(x-h)^2+k , where a, h, and k are integers g(x)= square

To find the translation of the function $f(x) = x^2$ 3 units down, we need to subtract 3 from the original function.<br /><br />The general form of a quadratic function is $a(x-h)^2+k$, where $a$, $h$, and $k$ are integers.<br /><br />In this case, the translation is 3 units down, so $k = -3$.<br /><br />Since there is no horizontal shift, $h = 0$.<br /><br />The coefficient $a$ remains the same as the original function, which is 1.<br /><br />Therefore, the translated function $g(x)$ is:<br /><br />$g(x) = 1(x-0)^2-3$<br /><br />Simplifying, we get:<br /><br />$g(x) = x^2 - 3$<br /><br />So, the answer is:<br /><br />$g(x) = x^2 - 3$