State the degree of the function and whether it is quadratic. f(t) = (t+6)^2 - t^2

To determine the degree of the function and whether it is quadratic, let's first simplify the expression for \( f(t) \):

\[
f(t) = (t + 6)^2 - t^2
\]

### Step 1: Expand the terms
First, expand \( (t + 6)^2 \):
\[
(t + 6)^2 = t^2 + 12t + 36
\]

Now substitute this into the original function:
\[
f(t) = (t^2 + 12t + 36) - t^2
\]

### Step 2: Simplify the expression
Simplify by canceling out the \( t^2 \) terms:
\[
f(t) = 12t + 36
\]

### Step 3: Determine the degree of the function
The simplified expression is \( f(t) = 12t + 36 \). This is a linear function because the highest power of \( t \) is 1. Therefore, the degree of the function is 1.

### Conclusion:
- The degree of the function is **1**.
- It is **not quadratic** (a quadratic function has a degree of 2).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the general form of a quadratic function?
2. How can you determine the degree of a polynomial?
3. What are the characteristics

Find out if the function f(t) = (t+6)^2 - t^2 is quadratic and learn how to determine its degree. This detailed explanation covers polynomial expansions and helps students understand the difference between linear and quadratic functions. Suitable for students in Grades 8-10.

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