4) Find g(x) where g(x) is the translation 5 units 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 \(f(x) = x^2\) by 5 units 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 asked to shift the graph of \(f(x) = x^2\) 5 units to the right. This means we need to replace \(h\) with -5 in the general form of the quadratic function.<br /><br />## Step 4<br />The function \(f(x) = x^2\) has no vertical shift, so \(k = 0\).<br /><br />## Step 5<br />The coefficient \(a\) in the general form of the quadratic function is the same as the coefficient of \(x^2\) in the original function \(f(x) = x^2\), which is 1.<br /><br />## Step 6<br />Substituting \(a = 1\), \(h = -5\), and \(k = 0\) into the quadratic function, we get \(g(x) = 1(x - (-5))^2 + 0\).<br /><br />## Step 7<br />Simplifying the above expression, we get \(g(x) = (x + 5)^2\).