(1) Find g(x) where g(x) is the translation 5 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

## Step 1<br />The problem asks us to find the function \(g(x)\), which is the translation of the function \(f(x)=x^{2}\) 5 units down. <br /><br />## Step 2<br />The general form of a quadratic function is \(a(x-h)^{2}+k\), where \(a\), \(h\), and \(k\) are integers. In this case, \(a\) is the coefficient of the \(x^{2}\) term, \(h\) is the horizontal shift, and \(k\) is the vertical shift.<br /><br />## Step 3<br />The function \(f(x)=x^{2}\) is a basic quadratic function with \(a=h=0\), and \(k=0\). <br /><br />## Step 4<br />When we translate this function 5 units down, the value of \(k\) decreases by 5. So, \(k\) becomes -5.<br /><br />## Step 5<br />Therefore, the function \(g(x)\) is \(x^{2}\) translated 5 units down, which is \(g(x)=x^{2}-5