Find the degree, leading term, leading coefficient, constant term, and end behavior of the given polynomial. \( f(x)=6 x+3 x^{2}-1 \) Degree: Leading term: Leading coefficient: End behavior: As \( x \rightarrow-\infty, f(x) \rightarrow \square \) As \( x \rightarrow \infty, f(x) \rightarrow \square \)

Let's analyze the polynomial \( f(x) = 6x + 3x^{2} - 1 \) to determine its degree, leading term, leading coefficient, constant term, and end behavior. ### 1. Degree: The **degree** of a polynomial is the highest power of the variable \( x \) in the polynomial. - **Degree:** \( 2 \) ### 2. Leading Term: The **leading term** is the term with the highest power of \( x \). - **Leading Term:** \( 3x^{2} \) ### 3. Leading Coefficient: The **leading coefficient** is the coefficient of the leading term. - **Leading Coefficient:** \( 3 \) ### 4. Constant Term: The **constant term** is the term without the variable \( x \). - **Constant Term:** \( -1 \) ### 5. End Behavior: The **end behavior** of a polynomial describes what happens to \( f(x) \) as \( x \) approaches positive or negative infinity. For \( f(x) = 3x^{2} + 6x - 1 \): - Since the degree is **even** and the leading coefficient is **positive**, both ends of the polynomial will point upwards. - **As \( x \rightarrow -\infty \), \( f(x) \rightarrow \infty \)** - **As \( x \rightarrow \infty \), \( f(x) \rightarrow \infty \)** ### Summary: - **Degree:** \( 2 \) - **Leading Term:** \( 3x^{2} \) - **Leading Coefficient:** \( 3 \) - **Constant Term:** \( -1 \) - **End Behavior:** - As \( x \rightarrow -\infty \), \( f(x) \rightarrow \infty \) - As \( x \rightarrow \infty \), \( f(x) \rightarrow \infty \)