The function \( h \) is defined as \( h(x)=-4 x^{2}+5 \). Find \( h(x+3) \). Write your answer without parentheses, and simplify it as much as possible. \( h(x+3)=\square \)

To find \( h(x+3) \), we substitute \( x+3 \) into the function \( h(x) \). Starting with: \[ h(x) = -4x^2 + 5 \] we substitute \( x \) with \( x+3 \): \[ h(x+3) = -4(x+3)^2 + 5 \] Next, we need to expand \( (x+3)^2 \): \[ (x+3)^2 = x^2 + 6x + 9 \] Now substituting this back, we have: \[ h(x+3) = -4(x^2 + 6x + 9) + 5 \] Distributing the \(-4\): \[ h(x+3) = -4x^2 - 24x - 36 + 5 \] Combining the constant terms: \[ h(x+3) = -4x^2 - 24x - 31 \] Thus, the simplified form is: \[ h(x+3) = -4x^2 - 24x - 31 \]