Question
Select the correct answer.
The graph shows the quadratic function f, and the table shows the quadratic function g.
A four-quadrant graph shows f of x, a parabola opens upward on the third quadrant of the graph. The edge point of the parabola is (-3, 1).
x -5 -4 -3 -2 -1 0 1
g(x) 10 7 6 7 10 15 22
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same minimum values.
B.
The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.
C.
The functions f and g have the same axis of symmetry, but the minimum value of f is greater than the minimum value of g.
D.
The functions f and g have different axes of symmetry and different minimum values.
The graph shows the quadratic function f, and the table shows the quadratic function g.
A four-quadrant graph shows f of x, a parabola opens upward on the third quadrant of the graph. The edge point of the parabola is (-3, 1).
x -5 -4 -3 -2 -1 0 1
g(x) 10 7 6 7 10 15 22
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same minimum values.
B.
The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.
C.
The functions f and g have the same axis of symmetry, but the minimum value of f is greater than the minimum value of g.
D.
The functions f and g have different axes of symmetry and different minimum values.
Answers
GPT-4o mini
To determine the correct answer, let's analyze the information provided:
1. **Function f** is a quadratic function represented by a parabola that opens upward. Its vertex (minimum point) is at the point (-3, 1). Since the vertex is at (-3, 1), the axis of symmetry of this parabola is the vertical line \( x = -3 \). The minimum value of f is 1.
2. **Function g** is represented by the values given in the table:
- At \( x = -5, g(-5) = 10 \)
- At \( x = -4, g(-4) = 7 \)
- At \( x = -3, g(-3) = 6 \)
- At \( x = -2, g(-2) = 7 \)
- At \( x = -1, g(-1) = 10 \)
- At \( x = 0, g(0) = 15 \)
- At \( x = 1, g(1) = 22 \)
The minimum value of g occurs at \( x = -3 \) where \( g(-3) = 6 \).
From this information:
- Both functions have the same axis of symmetry, which is \( x = -3 \).
- The minimum value of function f is 1.
- The minimum value of function g is 6.
Now, we can evaluate the statements:
A. **The functions f and g have the same axis of symmetry and the same minimum values.**
- Incorrect, as the minimum values are different (1 for f and 6 for g).
B. **The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.**
- Correct, since 1 (min of f) is less than 6 (min of g).
C. **The functions f and g have the same axis of symmetry, but the minimum value of f is greater than the minimum value of g.**
- Incorrect, as the minimum value of f is less than that of g.
D. **The functions f and g have different axes of symmetry and different minimum values.**
- Incorrect, as they have the same axis of symmetry.
Thus, the correct answer is **B. The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.**
1. **Function f** is a quadratic function represented by a parabola that opens upward. Its vertex (minimum point) is at the point (-3, 1). Since the vertex is at (-3, 1), the axis of symmetry of this parabola is the vertical line \( x = -3 \). The minimum value of f is 1.
2. **Function g** is represented by the values given in the table:
- At \( x = -5, g(-5) = 10 \)
- At \( x = -4, g(-4) = 7 \)
- At \( x = -3, g(-3) = 6 \)
- At \( x = -2, g(-2) = 7 \)
- At \( x = -1, g(-1) = 10 \)
- At \( x = 0, g(0) = 15 \)
- At \( x = 1, g(1) = 22 \)
The minimum value of g occurs at \( x = -3 \) where \( g(-3) = 6 \).
From this information:
- Both functions have the same axis of symmetry, which is \( x = -3 \).
- The minimum value of function f is 1.
- The minimum value of function g is 6.
Now, we can evaluate the statements:
A. **The functions f and g have the same axis of symmetry and the same minimum values.**
- Incorrect, as the minimum values are different (1 for f and 6 for g).
B. **The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.**
- Correct, since 1 (min of f) is less than 6 (min of g).
C. **The functions f and g have the same axis of symmetry, but the minimum value of f is greater than the minimum value of g.**
- Incorrect, as the minimum value of f is less than that of g.
D. **The functions f and g have different axes of symmetry and different minimum values.**
- Incorrect, as they have the same axis of symmetry.
Thus, the correct answer is **B. The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.**