Question
the figure below shows a graph ofd a function of f(x) in the coordinate plane.
11
10
9 here down to
8
7
6
5 point here hill up to
4
3
2
1
0 here
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Part A:
Identify the following key features of the graph:
A. Vertex: (
,
)
B. Axis of symmetry : x=
C. y-intercept: (0,
)
C. x-intercepts from left to right: (
, 0) and (
, 0).
Question 2
Part B:
Provide a real-world example that would be represented by this function and tell what the key features: vertex, x intercepts, y intercept and the axis, above represent.
11
10
9 here down to
8
7
6
5 point here hill up to
4
3
2
1
0 here
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Part A:
Identify the following key features of the graph:
A. Vertex: (
,
)
B. Axis of symmetry : x=
C. y-intercept: (0,
)
C. x-intercepts from left to right: (
, 0) and (
, 0).
Question 2
Part B:
Provide a real-world example that would be represented by this function and tell what the key features: vertex, x intercepts, y intercept and the axis, above represent.
Answers
Answered by
GPT-4o mini
Based on your description of the graph of the function \( f(x) \), here is how to identify the key features:
### Part A:
1. **Vertex**:
- **A. Vertex**: To determine the vertex, we would typically look for the highest or lowest point on the graph (the "peak" or lowest "valley").
- **A. Vertex**: (Please fill in the coordinates based on your graph's visual inspection).
2. **Axis of Symmetry**:
- **B. Axis of symmetry**: This is a vertical line that passes through the vertex. It can be expressed as \( x = \text{(x-coordinate of the vertex)} \).
- **B. Axis of symmetry**: (Please provide the x-coordinate from the vertex).
3. **y-intercept**:
- **C. y-intercept**: This is the point where the graph crosses the y-axis, usually found when \( x = 0 \).
- **C. y-intercept**: (0, [the y-coordinate from the graph when \( x = 0 \)]).
4. **x-intercepts**:
- **C. x-intercepts from left to right**: These are the points where the graph crosses the x-axis (where \( f(x) = 0 \)).
- **C. x-intercepts from left to right**: ( [first x-intercept], 0) and ( [second x-intercept], 0).
### Part B:
For a real-world example represented by the function \( f(x) \):
**Example Scenario**: Consider a projectile being launched into the air, such as a basketball shot or a water fountain jet.
### Key Features Explained:
- **Vertex**: This point represents the maximum height reached by the basketball or fountain jet. It tells you the peak of the trajectory.
- **y-intercept**: This point indicates the initial height from which the projectile starts. For a basketball shot, it would signify the height of the ball at the moment it's shot.
- **x-intercepts**: These points signify when the basketball reaches the ground. In the context of the water fountain, the x-intercepts would represent when the water reaches ground level after being shot into the air.
- **Axis of symmetry**: This represents the symmetry of the trajectory. In the case of the basketball shot, it shows that the time taken to reach maximum height is equal to the time taken to come back down, assuming there's no air resistance or other forces acting differently.
To fill this out accurately, please reference your graph for specific values and coordinates.
### Part A:
1. **Vertex**:
- **A. Vertex**: To determine the vertex, we would typically look for the highest or lowest point on the graph (the "peak" or lowest "valley").
- **A. Vertex**: (Please fill in the coordinates based on your graph's visual inspection).
2. **Axis of Symmetry**:
- **B. Axis of symmetry**: This is a vertical line that passes through the vertex. It can be expressed as \( x = \text{(x-coordinate of the vertex)} \).
- **B. Axis of symmetry**: (Please provide the x-coordinate from the vertex).
3. **y-intercept**:
- **C. y-intercept**: This is the point where the graph crosses the y-axis, usually found when \( x = 0 \).
- **C. y-intercept**: (0, [the y-coordinate from the graph when \( x = 0 \)]).
4. **x-intercepts**:
- **C. x-intercepts from left to right**: These are the points where the graph crosses the x-axis (where \( f(x) = 0 \)).
- **C. x-intercepts from left to right**: ( [first x-intercept], 0) and ( [second x-intercept], 0).
### Part B:
For a real-world example represented by the function \( f(x) \):
**Example Scenario**: Consider a projectile being launched into the air, such as a basketball shot or a water fountain jet.
### Key Features Explained:
- **Vertex**: This point represents the maximum height reached by the basketball or fountain jet. It tells you the peak of the trajectory.
- **y-intercept**: This point indicates the initial height from which the projectile starts. For a basketball shot, it would signify the height of the ball at the moment it's shot.
- **x-intercepts**: These points signify when the basketball reaches the ground. In the context of the water fountain, the x-intercepts would represent when the water reaches ground level after being shot into the air.
- **Axis of symmetry**: This represents the symmetry of the trajectory. In the case of the basketball shot, it shows that the time taken to reach maximum height is equal to the time taken to come back down, assuming there's no air resistance or other forces acting differently.
To fill this out accurately, please reference your graph for specific values and coordinates.