4) Find g(x) , where g(x) is the translation 3 units left 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

## Step 1<br />The problem asks us to find the function \(g(x)\), which is the translation of the function \(f(x)=x^{2}\) three units 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, 'h' is 3, so we replace 'x' with '(x+3)' in the original function \(f(x)=x^{2}\). <br /><br />## Step 4<br />This gives us the function \(g(x)=(x+3)^{2}\). <br /><br />## Step 5<br />The problem asks for 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 -3 (since the function is translated 3 units to the left), and 'k' is 0 (since there is no vertical shift). <br /><br />## Step 7<br />So, the function \(g(x)\) in the form \(a(x-h)^{2}+k\) is \(g(x)=1(x+3)^{2}+0\).