Rewrite the function by completing the square. \( g(x)=4 x^{2}-16 x+7 \) \( g(x)=\square(x+\square)^{2}+\square \)

To rewrite the function \( g(x)=4x^2-16x+7 \) by completing the square, let's first factor out the 4 from the first two terms: \[ g(x) = 4(x^2 - 4x) + 7. \] Next, we complete the square inside the parentheses. We take half of the coefficient of \( x \) (which is -4), square it, and add and subtract it inside the parentheses: \[ g(x) = 4\left(x^2 - 4x + 4 - 4\right) + 7. \] This simplifies to: \[ g(x) = 4((x - 2)^2 - 4) + 7. \] Distributing the 4 gives us: \[ g(x) = 4(x - 2)^2 - 16 + 7. \] Finally, we combine the constants: \[ g(x) = 4(x - 2)^2 - 9. \] Thus, the completed square form is: \[ g(x) = 4(x - 2)^2 - 9. \] In the requested format, it would be: \( g(x)=\square(x-2)^{2}+\square \) So the two filled squares are: \( g(x)=4(x-2)^{2}-9 \) Meaning you have \( g(x) = 4 \), \( (x-2) \), and \( -9 \) in the placeholders.