Question

Describe the end behavior of the quadratic function graphed below.



(2 points)
As x
approaches −∞
, f(x)
approaches
.

As x
approaches ∞
, f(x)
approaches

Answer 1

To describe the end behavior of a quadratic function, we generally consider the standard form of the quadratic function, which is \( f(x) = ax^2 + bx + c \).

1. If the leading coefficient \( a > 0 \):
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( +\infty \).
- As \( x \) approaches \( +\infty \), \( f(x) \) approaches \( +\infty \).

2. If the leading coefficient \( a < 0 \):
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \).
- As \( x \) approaches \( +\infty \), \( f(x) \) approaches \( -\infty \).

Please apply the above rules based on the specific function's leading coefficient you are analyzing:

- If \( a > 0 \):
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( +\infty \).
- As \( x \) approaches \( +\infty \), \( f(x) \) approaches \( +\infty \).

- If \( a < 0 \):
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \).
- As \( x \) approaches \( +\infty \), \( f(x) \) approaches \( -\infty \).

You can fill in the blanks in your description based on the sign of \( a \) once you identify the leading coefficient of your quadratic function.