Find and simplify $$ f(x+h) $$. Simplify your answer. $$ f(x)=-7 x^{2}-5 x+3 $$ $$ f(x+h)= $$

Question

UpStudy AI · Accepted Answer

To find and simplify $$ f(x+h) $$ for the function $$ f(x) = -7x^2 - 5x + 3 $$, follow these steps:

1. **Substitute $$ x $$ with $$ x + h $$ in the function:**
   $$
   f(x+h) = -7(x+h)^2 - 5(x+h) + 3
   $$

2. **Expand the squared term and distribute the coefficients:**
   $$
   f(x+h) = -7(x^2 + 2xh + h^2) - 5x - 5h + 3
   $$

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

4. **Combine like terms:**
   $$
   f(x+h) = -7x^2 - (14h + 5)x - 7h^2 - 5h + 3
   $$

So, the simplified form of $$ f(x+h) $$ is:

$$
f(x+h) = -7x^2 - (14h + 5)x - 7h^2 - 5h + 3
$$

**Final Answer:**

After expanding, f(x + h) = –7 x² – (14 h + 5)x – 7 h² – 5 h + 3
$$ f(x+h) = -7x^2 - (14h + 5)x - 7h^2 - 5h + 3 $$

Find and simplify \( f(x+h) \). Simplify your answer. \[ f(x)=-7 x^{2}-5 x+3 \] \[ f(x+h)= \]