Question
Describe the end behavior of the quadratic function graphed below.
the main points are (-2,0) (0,4) (2,0)
(2 points)
As x approaches −∞, f(x) approaches ___.
As x approaches ∞, f(x) approaches ___.
the main points are (-2,0) (0,4) (2,0)
(2 points)
As x approaches −∞, f(x) approaches ___.
As x approaches ∞, f(x) approaches ___.
Answers
Answered by
GPT-4o mini
To describe the end behavior of the quadratic function given the points (-2,0), (0,4), and (2,0), we note that this function opens upwards (since the vertex at (0,4) is the maximum point).
1. **As \( x \) approaches \(-\infty\), \( f(x) \) approaches \( \infty \).**
This is because as you move to the left on the graph (in the negative direction), the values of \( f(x) \) will continue to rise due to the upward-opening parabola.
2. **As \( x \) approaches \( \infty\), \( f(x) \) approaches \( \infty \).**
Similarly, as you move to the right on the graph (in the positive direction), the values of \( f(x) \) will also rise, reflecting the upward-opening nature of the parabola.
Putting it together:
- As \( x \) approaches \(-\infty\), \( f(x) \) approaches \( \infty \).
- As \( x \) approaches \( \infty\), \( f(x) \) approaches \( \infty \).
1. **As \( x \) approaches \(-\infty\), \( f(x) \) approaches \( \infty \).**
This is because as you move to the left on the graph (in the negative direction), the values of \( f(x) \) will continue to rise due to the upward-opening parabola.
2. **As \( x \) approaches \( \infty\), \( f(x) \) approaches \( \infty \).**
Similarly, as you move to the right on the graph (in the positive direction), the values of \( f(x) \) will also rise, reflecting the upward-opening nature of the parabola.
Putting it together:
- As \( x \) approaches \(-\infty\), \( f(x) \) approaches \( \infty \).
- As \( x \) approaches \( \infty\), \( f(x) \) approaches \( \infty \).