Question

Question
Describe the end behavior of the quadratic function graphed below.


y=-x^2 +4
(2 points)
As x
approaches −∞
, f(x)
approaches
.

As x
approaches ∞
, f(x)
approaches
.

Answer 1

To analyze the end behavior of the quadratic function \( y = -x^2 + 4 \):

1. **As \( x \) approaches \( -\infty \)**:
- Since the leading term is \( -x^2 \), as \( x \) becomes very large in the negative direction, the \( -x^2 \) term will dominate and head towards \( -\infty \).
- Therefore, \( f(x) \) approaches \( -\infty \).

2. **As \( x \) approaches \( \infty \)**:
- Similarly, as \( x \) becomes very large in the positive direction, the \( -x^2 \) term again dominates and goes towards \( -\infty \).
- Therefore, \( f(x) \) also approaches \( -\infty \).

In summary:

- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \).
- As \( x \) approaches \( \infty \), \( f(x) \) approaches \( -\infty \).