Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Transcription for Educational Website:**
---
**Question:**
- From where to where is the red bird in the air?
---
*Note: This content does not contain any graphs or diagrams that require detailed explanation.*
![### Task 1
#### RED BIRD
1. **What is the maximum height your bird flew?**
The maximum height is (21, 28).
2. **What was the total horizontal distance your bird traveled?**
The total distance is 34.
3. **What is the equation for the axis of symmetry?**
The axis of symmetry is \(x = h\).
Given the equation of the parabola:
\[
y = a (x - h)^2 + k
\]
Substituting the given maximum height:
\[
y = -\frac{28}{289}(x - 21)^2 + 28
\]
Hence, the axis of symmetry \(x = 21\).
### Diagram Explanation
There is a diagram demonstrating a parabolic trajectory, showing the bird's flight path. The flight starts at the point (4, 0) and ends at (38, 0). The vertex, which represents the highest point, is marked at (21, 28).
### Detailed Steps:
#### Finding the Vertex:
To maximize the height, the vertex form of the parabola is used:
\[
y = a (x - h)^2 + k
\]
Where (h, k) is the vertex. Substituting:
\[
y = -\frac{28}{289}(x - 21)^2 + 28
\]
#### Calculating Total Horizontal Distance:
The horizontal distance is calculated between the start point (4,0) and the end point (38,0):
\[
38 - 4 = 34
\]
### Summary:
The maximum height achieved by the red bird during its flight is 28 units at a horizontal distance of 21 units from the starting point. The total horizontal distance covered by the bird is 34 units. The equation representing the axis of symmetry is \( x = 21 \). The trajectory of the bird is parabolic, and it can be expressed by the equation \( y = -\frac{28}{289}(x - 21)^2 + 28 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe69ae420-f527-4e45-9bd3-7e5ab3edfa8c%2F1c143fd8-640a-4058-b3c6-ff9a886ef360%2F9gjxhfp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Task 1
#### RED BIRD
1. **What is the maximum height your bird flew?**
The maximum height is (21, 28).
2. **What was the total horizontal distance your bird traveled?**
The total distance is 34.
3. **What is the equation for the axis of symmetry?**
The axis of symmetry is \(x = h\).
Given the equation of the parabola:
\[
y = a (x - h)^2 + k
\]
Substituting the given maximum height:
\[
y = -\frac{28}{289}(x - 21)^2 + 28
\]
Hence, the axis of symmetry \(x = 21\).
### Diagram Explanation
There is a diagram demonstrating a parabolic trajectory, showing the bird's flight path. The flight starts at the point (4, 0) and ends at (38, 0). The vertex, which represents the highest point, is marked at (21, 28).
### Detailed Steps:
#### Finding the Vertex:
To maximize the height, the vertex form of the parabola is used:
\[
y = a (x - h)^2 + k
\]
Where (h, k) is the vertex. Substituting:
\[
y = -\frac{28}{289}(x - 21)^2 + 28
\]
#### Calculating Total Horizontal Distance:
The horizontal distance is calculated between the start point (4,0) and the end point (38,0):
\[
38 - 4 = 34
\]
### Summary:
The maximum height achieved by the red bird during its flight is 28 units at a horizontal distance of 21 units from the starting point. The total horizontal distance covered by the bird is 34 units. The equation representing the axis of symmetry is \( x = 21 \). The trajectory of the bird is parabolic, and it can be expressed by the equation \( y = -\frac{28}{289}(x - 21)^2 + 28 \).
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