4) Find g(x) where g(x) is the translation 1 unit right 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 a translation of the function \(f(x) = x^2\) one unit to the right. <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 form, \(h\) represents the horizontal shift of the graph. If \(h\) is positive, the graph shifts to the right; if \(h\) is negative, the graph shifts to the left.<br /><br />## Step 3<br />In this case, we are asked to shift the graph one unit to the right. This means we need to replace \(h\) with \(-1\) in the general form of the quadratic function. <br /><br />## Step 4<br />The function \(f(x) = x^2\) has \(a = 1\), \(h = 0\), and \(k = 0\). When we shift the graph one unit to the right, \(h\) becomes \(-1\), but \(a\) and \(k\) remain the same.<br /><br />## Step 5<br />So, the function \(g(x)\) becomes \(g(x) = 1(x - (-1))^2 + 0\), which simplifies to \(g(x) = (x + 1)^2\).