\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}

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Evaluate the expression by following steps:
- step0: Evaluate:
  $$-7\left(x+h\right)^{2}-5\left(x+h\right)+3$$
- step1: Substitute:
  $$-7\left(x+0\right)^{2}-5\left(x+0\right)+3$$
- step2: Remove 0:
  $$-7x^{2}-5\left(x+0\right)+3$$
- step3: Remove 0:
  $$-7x^{2}-5x+3$$
Substitute $$ h=1 $$ into the expression $$ -7(x+h)^{2}-5(x+h)+3 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$-7\left(x+h\right)^{2}-5\left(x+h\right)+3$$
- step1: Substitute:
  $$-7\left(x+1\right)^{2}-5\left(x+1\right)+3$$
- step2: Expand the expression:
  $$-7x^{2}-14x-7-5\left(x+1\right)+3$$
- step3: Expand the expression:
  $$-7x^{2}-14x-7-5x-5+3$$
- step4: Subtract the terms:
  $$-7x^{2}-19x-9$$
Substitute $$ h=2 $$ into the expression $$ -7(x+h)^{2}-5(x+h)+3 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$-7\left(x+h\right)^{2}-5\left(x+h\right)+3$$
- step1: Substitute:
  $$-7\left(x+2\right)^{2}-5\left(x+2\right)+3$$
- step2: Expand the expression:
  $$-7x^{2}-28x-28-5\left(x+2\right)+3$$
- step3: Expand the expression:
  $$-7x^{2}-28x-28-5x-10+3$$
- step4: Subtract the terms:
  $$-7x^{2}-33x-35$$
Expand the expression $$ -7(x+h)^{2}-5(x+h)+3 $$
Simplify the expression by following steps:
- step0: Calculate:
  $$-7\left(x+h\right)^{2}-5\left(x+h\right)+3$$
- step1: Expand the expression:
  $$-7x^{2}-14xh-7h^{2}-5\left(x+h\right)+3$$
- step2: Expand the expression:
  $$-7x^{2}-14xh-7h^{2}-5x-5h+3$$
To find and simplify $$ f(x+h) $$ for the function $$ f(x) = -7x^2 - 5x + 3 $$, we will substitute $$ x+h $$ into the function and simplify the expression step by step.

1. **Substituting $$ x+h $$ into $$ f(x) $$**:
   $$
   f(x+h) = -7(x+h)^2 - 5(x+h) + 3
   $$

2. **Expanding $$ (x+h)^2 $$**:
   $$
   (x+h)^2 = x^2 + 2xh + h^2
   $$
   Therefore,
   $$
   f(x+h) = -7(x^2 + 2xh + h^2) - 5(x+h) + 3
   $$

3. **Distributing the terms**:
   $$
   f(x+h) = -7x^2 - 14xh - 7h^2 - 5x - 5h + 3
   $$

4. **Combining like terms**:
   The expression simplifies to:
   $$
   f(x+h) = -7x^2 - (14h + 5)x - (7h^2 + 5h - 3)
   $$

Thus, the simplified form of $$ f(x+h) $$ is:
$$
\boxed{-7x^2 - 14xh - 7h^2 - 5x - 5h + 3}
$$
$$ f(x+h) = -7x^2 - 14xh - 7h^2 - 5x - 5h + 3 $$

\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}

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