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 1The 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. ## Step 2The general form of a quadratic function is \(a(x-h)^2 + k\), where , , and are integers. In this form, represents the horizontal shift of the graph. If is positive, the graph shifts to the right; if is negative, the graph shifts to the left.## Step 3In this case asked to shift the graph of \(f(x) = x^2\) 5 units to the right. This means we need to replace with -5 in the general form of the quadratic function.## Step 4The function \(f(x) = x^2\) has no vertical shift, so .## Step 5The coefficient in the general form of the quadratic function is the same as the coefficient of in the original function \(f(x) = x^2\), which is 1.## Step 6Substituting , , and into the quadratic function, we get \(g(x) = 1(x - (-5))^2 + 0\).## Step 7Simplifying the above expression, we get \(g(x) = (x + 5)^2\).