4) Find g(x) , where g(x) is the reflection across the x-axis of f(x)=x^2 1)) Write your answer in the form a(x-h)^2+k where a, h, and k are integ g(x)= square

To find the reflection of the function $f(x) = x^2$ across the x-axis, we need to reflect the graph of $f(x)$ over the x-axis.<br /><br />The reflection of a function $f(x)$ across the x-axis is given by $-f(x)$.<br /><br />So, the reflection of $f(x) = x^2$ across the x-axis is $g(x) = -x^2$.<br /><br />Now, we need to write the answer in the form $a(x-h)^2+k$, where $a$, $h$, and $k$ are integers.<br /><br />In this case, $a = -1$, $h = 0$, and $k = 0$.<br /><br />Therefore, the answer is $g(x) = -(x-0)^2+0$, which simplifies to $g(x) = -x^2$.<br /><br />So, the final answer is $g(x) = -x^2$.