1. The problem asks us to rewrite the quadratic function \( g(x) = 5x^2 + 20x - 12 \) in the form \( g(x) = a(x+h)^2 + k \), where \(a, h, k\) are integers. 2. Start with the original function: \( g(x) = 5x^2 + 20x - 12 \). 3. Factor out the coefficient 5 from the first two terms to prepare for completing the square: $$ g(x) = 5(x^2 + 4x) - 12 $$ 4. Complete the square inside the parentheses. The expression inside is \( x^2 + 4x \). 5. Take half of the coefficient of \(x\), which is 4, so half is 2. 6. Square 2 to get 4, then add and subtract 4 inside the parentheses to complete the square: $$ g(x) = 5(x^2 + 4x + 4 - 4) - 12 $$ 7. Rewrite as: $$ g(x) = 5\left( (x + 2)^2 - 4 \right) - 12 $$ 8. Distribute the 5: $$ g(x) = 5(x + 2)^2 - 20 - 12 $$ 9. Simplify constants: $$ g(x) = 5(x + 2)^2 - 32 $$ 10. Thus, the function in the desired form is: $$ g(x) = 5(x + 2)^2 - 32 $$ where \( a = 5 \), \( h = 2 \), and \( k = -32 \).