Question
the figure below shows a graph ofd a function of f(x) in the coordinate plane.
11
10
9 ________________(9,0.5)
8
7
6
5 _5,0
4
3
2
1
0 ______________________________________here (0, 1.25)
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 ________________(9,0.5)
8
7
6
5 _5,0
4
3
2
1
0 ______________________________________here (0, 1.25)
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
Sure! Let's analyze the provided information regarding the graph representing the function \( f(x) \). Since I can’t see the graph itself, I’ll give you a template based on typical features of quadratic functions.
### Part A: Features of the Graph
A. **Vertex**: The vertex is the point where the parabola changes direction. Based on typical values, let’s assume a hypothetical vertex (let's assume it's located at \( (h, k) \)), pick appropriate values based on the given context or your graph.
B. **Axis of Symmetry**: This is a vertical line that runs through the vertex, given by the formula \( x = h \).
C. **y-intercept**: The y-intercept is where the graph crosses the y-axis, typically at the point \( (0, k) \). You mentioned point (0, 1.25), so we assume this is the y-intercept.
D. **x-intercepts from left to right**: These points are where the graph crosses the x-axis, represented as \( (x_1, 0) \) and \( (x_2, 0) \). In your case, from the provided coordinates, you have \( (5, 0) \) and \( (9, 0.5) \) (which looks like it might be on the wrong axis but will proceed with these values assuming additional approximations).
### Summary (Hypothetical Values):
- A. Vertex: \( (x_v, y_v) \)
- B. Axis of symmetry: \( x = x_v \)
- C. y-intercept: (0, 1.25)
- D. x-intercepts from left to right: \( (5, 0) \) and \( (9, 0.5) \)
### Part B: Real-world Example
**Example**: Let’s say the function \( f(x) \) describes the path of a projectile fired from a certain height—like a basketball shot.
**Key Features**:
- **Vertex**: This represents the maximum height the basketball reaches (the peak of its trajectory) before descending again. If the vertex were \( (h, k) \), it means the highest point is at \( h \) seconds after the ball is thrown, and at that moment, the height is \( k \) meters.
- **x-intercepts**: These represent the moments when the ball is at ground level (height = 0). For example, they could signify the times of flight: 5 seconds (first point of contact) and approximately 9 seconds (when it hits the ground again).
- **y-intercept**: This indicates the initial height from which the basketball is thrown—here, it is 1.25 meters, meaning the ball is released from a height of 1.25 meters above the ground.
- **Axis of symmetry**: This reflects that the motion of the basketball is symmetric around the peak height, indicating that the time taken to reach its highest point is equal to the time taken to come back down to ground level.
Feel free to adjust the values according to the details of your specific graph!
### Part A: Features of the Graph
A. **Vertex**: The vertex is the point where the parabola changes direction. Based on typical values, let’s assume a hypothetical vertex (let's assume it's located at \( (h, k) \)), pick appropriate values based on the given context or your graph.
B. **Axis of Symmetry**: This is a vertical line that runs through the vertex, given by the formula \( x = h \).
C. **y-intercept**: The y-intercept is where the graph crosses the y-axis, typically at the point \( (0, k) \). You mentioned point (0, 1.25), so we assume this is the y-intercept.
D. **x-intercepts from left to right**: These points are where the graph crosses the x-axis, represented as \( (x_1, 0) \) and \( (x_2, 0) \). In your case, from the provided coordinates, you have \( (5, 0) \) and \( (9, 0.5) \) (which looks like it might be on the wrong axis but will proceed with these values assuming additional approximations).
### Summary (Hypothetical Values):
- A. Vertex: \( (x_v, y_v) \)
- B. Axis of symmetry: \( x = x_v \)
- C. y-intercept: (0, 1.25)
- D. x-intercepts from left to right: \( (5, 0) \) and \( (9, 0.5) \)
### Part B: Real-world Example
**Example**: Let’s say the function \( f(x) \) describes the path of a projectile fired from a certain height—like a basketball shot.
**Key Features**:
- **Vertex**: This represents the maximum height the basketball reaches (the peak of its trajectory) before descending again. If the vertex were \( (h, k) \), it means the highest point is at \( h \) seconds after the ball is thrown, and at that moment, the height is \( k \) meters.
- **x-intercepts**: These represent the moments when the ball is at ground level (height = 0). For example, they could signify the times of flight: 5 seconds (first point of contact) and approximately 9 seconds (when it hits the ground again).
- **y-intercept**: This indicates the initial height from which the basketball is thrown—here, it is 1.25 meters, meaning the ball is released from a height of 1.25 meters above the ground.
- **Axis of symmetry**: This reflects that the motion of the basketball is symmetric around the peak height, indicating that the time taken to reach its highest point is equal to the time taken to come back down to ground level.
Feel free to adjust the values according to the details of your specific graph!