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What is the end behavior of function h? h(x)\:=\:\textrm{-}4x^{2}\:+\:11 As x approaches negative infinity, h(x) approaches As x approaches positive infinity, h(x)
 approaches 

To determine the end behavior of the function \( h(x) = -4x^2 + 11 \), we analyze the leading term, which is the term with the highest power of \( x \).

### Step 1: Identify the Leading Term
The leading term in \( h(x) \) is \( -4x^2 \).

### Step 2: Determine End Behavior
- As \( x \) approaches negative infinity (\( x \to -\infty \)):
  - Since the leading term is \( -4x^2 \), and the coefficient \( -4 \) is negative, \( h(x) \) will approach negative infinity.
  
- As \( x \) approaches positive infinity (\( x \to \infty \)):
  - Similarly, since the leading term \( -4x^2 \) dominates and the coefficient is negative, \( h(x) \) will also approach negative infinity.

### Final Answers:
- As \( x \) approaches negative infinity, \( h(x) \) approaches **negative infinity**.
- As \( x \) approaches positive infinity, \( h(x) \) approaches **negative infinity**.

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Here are 5 related questions:
1. What would the end behavior be if the coefficient of \( x^2 \) were positive?
2. How does the constant term \( +11 \) affect the function's end behavior?
3. What is the significance of the leading term in determining end behavior?
4. How would the graph of \( h(x) \) compare to the graph of \( y = x^2 \)?
5. What happens to the end behavior if the exponent in the leading term is odd?

**Tip:** When analyzing end behavior, always focus on the leading term of the polynomial, as it dominates the behavior of the function for large values of \( |x| \).

Explore the end behavior of the polynomial function h(x) = -4x^2 + 11 as x approaches negative and positive infinity. Learn how the leading term and coefficients affect the function's behavior. Suitable for high school students studying polynomial functions and end behavior.

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