Question
Find the equation of the given graph.
Question content area bottom left
Part 1
Choose the correct equation.
A.y equals negative StartRoot x minus 2 EndRoot plus 1
y equals negative StartRoot x minus 2 EndRoot plus 1
B.y equals StartRoot x minus 2 EndRoot plus 1
y equals StartRoot x minus 2 EndRoot plus 1
C.y equals negative StartRoot x EndRoot minus 2 plus 1
y equals negative StartRoot x EndRoot minus 2 plus 1
.
.
.
Question content area right
Part 1
-10
10
-10
10
x
y
Question content area bottom left
Part 1
Choose the correct equation.
A.y equals negative StartRoot x minus 2 EndRoot plus 1
y equals negative StartRoot x minus 2 EndRoot plus 1
B.y equals StartRoot x minus 2 EndRoot plus 1
y equals StartRoot x minus 2 EndRoot plus 1
C.y equals negative StartRoot x EndRoot minus 2 plus 1
y equals negative StartRoot x EndRoot minus 2 plus 1
.
.
.
Question content area right
Part 1
-10
10
-10
10
x
y
Answers
GPT-4o mini
To find the correct equation for the given graph, we need to analyze the options provided in relation to the behavior and characteristics of square root functions.
### Analyzing the Given Options:
1. **A. \(y = -\sqrt{x - 2} + 1\)**:
- This describes a downward-opening square root function starting at the point \( (2, 1) \). The negative sign indicates that the graph will be reflected over the x-axis.
2. **B. \(y = \sqrt{x - 2} + 1\)**:
- This describes an upward-opening square root function starting at the point \( (2, 1) \). The graph will increase to the right.
3. **C. \(y = -\sqrt{x} - 2 + 1\)**:
- This describes a downward-opening square root function starting at the origin but shifted down.
### Determining Characteristics Based on the Graph:
- Check the starting point of the graph:
- If the graph starts at \( (2, 1) \), it suggests the use of \( \sqrt{x - 2} \).
- Check the direction of the graph:
- If the graph decreases to the right (goes down), then it must have a negative coefficient for the square root.
### Conclusion:
- If the graph starts at \( (2, 1) \) and decreases as you move to the right, the correct option would be **A**: \(y = -\sqrt{x - 2} + 1\).
Without seeing the actual graph, choose option **A** if the graph starts at (2, 1) and goes downward. Otherwise, choose according to the observed behavior of the graph.
### Analyzing the Given Options:
1. **A. \(y = -\sqrt{x - 2} + 1\)**:
- This describes a downward-opening square root function starting at the point \( (2, 1) \). The negative sign indicates that the graph will be reflected over the x-axis.
2. **B. \(y = \sqrt{x - 2} + 1\)**:
- This describes an upward-opening square root function starting at the point \( (2, 1) \). The graph will increase to the right.
3. **C. \(y = -\sqrt{x} - 2 + 1\)**:
- This describes a downward-opening square root function starting at the origin but shifted down.
### Determining Characteristics Based on the Graph:
- Check the starting point of the graph:
- If the graph starts at \( (2, 1) \), it suggests the use of \( \sqrt{x - 2} \).
- Check the direction of the graph:
- If the graph decreases to the right (goes down), then it must have a negative coefficient for the square root.
### Conclusion:
- If the graph starts at \( (2, 1) \) and decreases as you move to the right, the correct option would be **A**: \(y = -\sqrt{x - 2} + 1\).
Without seeing the actual graph, choose option **A** if the graph starts at (2, 1) and goes downward. Otherwise, choose according to the observed behavior of the graph.