Question
Question
Describe the intervals of increase/decrease for the quadratic function graphed below.
y=-(x-2)^2 +4
(4 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.
The quadratic function is increasing from Response area to Response area, and it is decreasing from Response area to Response area.
Describe the intervals of increase/decrease for the quadratic function graphed below.
y=-(x-2)^2 +4
(4 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.
The quadratic function is increasing from Response area to Response area, and it is decreasing from Response area to Response area.
Answers
Answered by
GPT-4o mini
To analyze the intervals of increase and decrease for the quadratic function \( y = -(x-2)^2 + 4 \):
1. **Identify the vertex**: The function is in vertex form \( y = a(x-h)^2 + k \). Here:
- \( h = 2 \)
- \( k = 4 \)
- The vertex is at the point \( (2, 4) \).
2. **Determine the direction of the parabola**: Since the coefficient of the squared term (which is -1) is negative, the parabola opens downwards.
3. **Determine intervals**:
- The function is **increasing** to the left of the vertex, from \( -\infty \) up to \( 2 \).
- The function is **decreasing** to the right of the vertex, from \( 2 \) to \( +\infty \).
Now we can fill in the responses:
1. The quadratic function is increasing from **\(-\infty\)** to **2**.
2. The quadratic function is decreasing from **2** to **\(+\infty\)**.
So the complete answer would be:
- The quadratic function is increasing from **\(-\infty\)** to **2**, and it is decreasing from **2** to **\(+\infty\)**.
1. **Identify the vertex**: The function is in vertex form \( y = a(x-h)^2 + k \). Here:
- \( h = 2 \)
- \( k = 4 \)
- The vertex is at the point \( (2, 4) \).
2. **Determine the direction of the parabola**: Since the coefficient of the squared term (which is -1) is negative, the parabola opens downwards.
3. **Determine intervals**:
- The function is **increasing** to the left of the vertex, from \( -\infty \) up to \( 2 \).
- The function is **decreasing** to the right of the vertex, from \( 2 \) to \( +\infty \).
Now we can fill in the responses:
1. The quadratic function is increasing from **\(-\infty\)** to **2**.
2. The quadratic function is decreasing from **2** to **\(+\infty\)**.
So the complete answer would be:
- The quadratic function is increasing from **\(-\infty\)** to **2**, and it is decreasing from **2** to **\(+\infty\)**.