Evaluate the functions f(x) =3x^2-2 at each specific value and simplify f(x+1)


Let's evaluate \( f(x) = 3x^2 - 2 \) at each specific value and simplify \( f(x+1) \).

### 1. Evaluating \( f(x+1) \):

We are asked to find \( f(x+1) \), which means we substitute \( x+1 \) into the function wherever \( x \) appears:

\[
f(x+1) = 3(x+1)^2 - 2
\]

First, expand \( (x+1)^2 \):

\[
(x+1)^2 = x^2 + 2x + 1
\]

Now substitute this into the function:

\[
f(x+1) = 3(x^2 + 2x + 1) - 2
\]

Distribute the 3:

\[
f(x+1) = 3x^2 + 6x + 3 - 2
\]

Simplify:

\[
f(x+1) = 3x^2 + 6x + 1
\]

So, \( f(x+1) = 3x^2 + 6x + 1 \).

### Do you have any questions or need further details?

Here are five related questions to expand on this topic:

1. What happens if you evaluate \( f(-1) \) in the same function?
2. How would you approach solving \( f(2) \) for this function?
3. Can you simplify \( f(x-1) \) instead of \( f(x+1) \)?
4. How would the graph of \( f(x) = 3x^2 - 2 \) look?
5. What are the roots of the equation \( f(x) = 0 \)?

**Tip:** When evaluating functions at shifted values like \( f(x+1) \), always substitute carefully and simplify step by step to avoid mistakes.

Evaluate the functions f(x) = 3x^2 - 2 at each specific value and simplify f(x+1).

Learn how to simplify and evaluate the polynomial function f(x) = 3x^2 - 2 at f(x+1). This step-by-step guide walks through substitution and simplification, covering key algebraic concepts in polynomial function evaluation. Ideal for students in Grades 9-10.

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