Question
Use the graph below to describe the end behavior and intervals of increase/decrease for the quadratic function.
(-1,0) (0,4) (1.5,6.25) (4,0)
(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A) End Behavior:
as x approaches −∞, f(x) approaches
Response area
as x approaches ∞, f(x) approaches
Response area
B) Intervals of Increase/Decrease:
The quadratic function is increasing from Response area to Response area,
and is decreasing from Response area to Response area.
(-1,0) (0,4) (1.5,6.25) (4,0)
(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A) End Behavior:
as x approaches −∞, f(x) approaches
Response area
as x approaches ∞, f(x) approaches
Response area
B) Intervals of Increase/Decrease:
The quadratic function is increasing from Response area to Response area,
and is decreasing from Response area to Response area.
Answers
GPT-4o mini
To analyze the end behavior and the intervals of increase/decrease for the given quadratic function defined by the points (-1,0), (0,4), (1.5,6.25), and (4,0), we can follow the characteristics of quadratic functions.
A) End Behavior:
1. As x approaches −∞, f(x) approaches **∞** (the parabola opens upwards, as indicated by the vertex being at a higher point).
2. As x approaches ∞, f(x) approaches **∞** (the parabola continues to rise as x increases).
B) Intervals of Increase/Decrease:
1. The quadratic function is increasing from **0** (where the vertex is at its maximum) to **4** (where it returns to y = 0 as x moves to the right),
2. and is decreasing from **-1** (where y = 0) to **0** (where the vertex is).
Putting it all together:
A) End Behavior:
as x approaches −∞, f(x) approaches **∞**
as x approaches ∞, f(x) approaches **∞**
B) Intervals of Increase/Decrease:
The quadratic function is increasing from **0** to **4**,
and is decreasing from **-1** to **0**.
A) End Behavior:
1. As x approaches −∞, f(x) approaches **∞** (the parabola opens upwards, as indicated by the vertex being at a higher point).
2. As x approaches ∞, f(x) approaches **∞** (the parabola continues to rise as x increases).
B) Intervals of Increase/Decrease:
1. The quadratic function is increasing from **0** (where the vertex is at its maximum) to **4** (where it returns to y = 0 as x moves to the right),
2. and is decreasing from **-1** (where y = 0) to **0** (where the vertex is).
Putting it all together:
A) End Behavior:
as x approaches −∞, f(x) approaches **∞**
as x approaches ∞, f(x) approaches **∞**
B) Intervals of Increase/Decrease:
The quadratic function is increasing from **0** to **4**,
and is decreasing from **-1** to **0**.