(J) Find g(x) where g(x) is the translation 1 unit left of f(x)=x^2 1)) Write your answer in the form a(x-h)^2+k , where a, h, and k are integers. g(x)= square

## Step 1<br />The problem asks us to find the function \(g(x)\), which is the translation of the function \(f(x)=x^{2}\) one unit to the left. <br /><br />## Step 2<br />In function transformations, a translation to the left by 'h' units is represented by replacing 'x' with '(x+h)' in the original function. <br /><br />## Step 3<br />In this case, the translation is one unit to the left, so 'h' is 1. <br /><br />## Step 4<br />Substituting 'x' with '(x+1)' in the original function \(f(x)=x^{2}\), we get \(g(x)=(x+1)^{2}\).<br /><br />## Step 5<br />The problem asks us to write the answer in the form \(a(x-h)^{2}+k\), where 'a', 'h', and 'k' are integers. <br /><br />## Step 6<br />In this case, 'a' is 1 (since there is no coefficient in front of the squared term), 'h' is -1 (since the translation is one unit to the left), and 'k' is 0 (since there is no constant term). <br /><br />## Step 7<br />So, the function \(g(x)\) in the form \(a(x-h)^{2}+k\) is \(g(x)=1(x+1)^{2}+0\).