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