\begin{tabular}{l} Find and simplify \( f(x+h) \). Simplify your answer. \\ \( \qquad f(x)=-7 x^{2}-5 x+3 \) \\ \( \qquad f(x+h)=\square \) \\ \hline\( \square \) \\ \hline\end{tabular}

To find \( f(x+h) \), we substitute \( x+h \) into the function \( f(x) = -7x^2 - 5x + 3 \): \[ f(x+h) = -7(x+h)^2 - 5(x+h) + 3 \] Now we simplify each part. First, expand \( (x+h)^2 \): \[ (x+h)^2 = x^2 + 2xh + h^2 \] Substituting back, we have: \[ f(x+h) = -7(x^2 + 2xh + h^2) - 5(x + h) + 3 \] Expanding this gives: \[ f(x+h) = -7x^2 - 14xh - 7h^2 - 5x - 5h + 3 \] Now, we can combine like terms: \[ f(x+h) = -7x^2 - (14h + 5)x - (7h^2 + 5h - 3) \] Thus, the final simplified answer is: \[ f(x+h) = -7x^2 - (14h + 5)x - (7h^2 + 5h - 3) \]