Question
The quadratic function f has a vertex at (3,4) and opens upward. The quadratic function g is shown below.
Which statement is true?
A.
The minimum value of f is greater than the minimum value of g.
B.
The minimum value of g is greater than the minimum value of f.
C.
The maximum value of g is greater than the maximum value of f.
D.
The maximum value of f is greater than the maximum value of g.
Which statement is true?
A.
The minimum value of f is greater than the minimum value of g.
B.
The minimum value of g is greater than the minimum value of f.
C.
The maximum value of g is greater than the maximum value of f.
D.
The maximum value of f is greater than the maximum value of g.
Answers
GPT-4o mini
To analyze the statements regarding the quadratic functions \( f \) and \( g \), we can extract the following information:
1. The vertex of the quadratic function \( f \) is at the point \( (3, 4) \) and since it opens upward, the minimum value of \( f \) is at its vertex, which is \( 4 \).
2. The nature of \( g \) is not stated explicitly in your question, but if \( g \) is a quadratic function and we assume it opens downward, the maximum value would occur at its vertex, and if it opens upward, it would have a minimum value much like \( f \).
Depending on the unspecified characteristics of \( g \), we analyze the provided statements:
- **Statement A:** The minimum value of \( f \) (which is \( 4 \)) is greater than the minimum value of \( g \). This can only be true if \( g \) opens upward and has a minimum value that is less than \( 4 \).
- **Statement B:** The minimum value of \( g \) is greater than the minimum value of \( f \). This can be true if \( g \) opens upward with a minimum greater than \( 4 \).
- **Statement C:** The maximum value of \( g \) is greater than the maximum value of \( f \). This can only apply if \( g \) opens downward and has a larger maximum than \( f \), but since \( f \) opens upward and does not have a maximum value, this would likely be irrelevant without more information about \( g \).
- **Statement D:** The maximum value of \( f \) is greater than the maximum value of \( g \). Similar to Statement C, if \( g \) opens upward, then \( f \) which does not have a maximum value does not make this comparison valid.
Since you haven't provided specific information about \( g \), but if we assume \( g \) is a quadratic function that opens upward (the most direct comparison), we are inclined to conclude:
- **If \( g \) opens upward and has its vertex below \( 4 \), then A is true.**
- **If \( g \) opens upward and has its vertex above \( 4 \), then B is true.**
- If \( g \) opens downward, then statements C and D refer to maximum values that may not have a valid comparison.
So, based on typical expectations without specific details of \( g \), the safest assumption is that statement A or B may be true depending on the exact nature of \( g \); if \( g \) opens upward and has a minimum greater than \( 4\), then B will be correct.
In summary:
- **If no additional information is available about function \( g \)**, we can conclude the accurate answer is contingent upon its characteristics and specifically its vertex value in comparison to \( 4\).
1. The vertex of the quadratic function \( f \) is at the point \( (3, 4) \) and since it opens upward, the minimum value of \( f \) is at its vertex, which is \( 4 \).
2. The nature of \( g \) is not stated explicitly in your question, but if \( g \) is a quadratic function and we assume it opens downward, the maximum value would occur at its vertex, and if it opens upward, it would have a minimum value much like \( f \).
Depending on the unspecified characteristics of \( g \), we analyze the provided statements:
- **Statement A:** The minimum value of \( f \) (which is \( 4 \)) is greater than the minimum value of \( g \). This can only be true if \( g \) opens upward and has a minimum value that is less than \( 4 \).
- **Statement B:** The minimum value of \( g \) is greater than the minimum value of \( f \). This can be true if \( g \) opens upward with a minimum greater than \( 4 \).
- **Statement C:** The maximum value of \( g \) is greater than the maximum value of \( f \). This can only apply if \( g \) opens downward and has a larger maximum than \( f \), but since \( f \) opens upward and does not have a maximum value, this would likely be irrelevant without more information about \( g \).
- **Statement D:** The maximum value of \( f \) is greater than the maximum value of \( g \). Similar to Statement C, if \( g \) opens upward, then \( f \) which does not have a maximum value does not make this comparison valid.
Since you haven't provided specific information about \( g \), but if we assume \( g \) is a quadratic function that opens upward (the most direct comparison), we are inclined to conclude:
- **If \( g \) opens upward and has its vertex below \( 4 \), then A is true.**
- **If \( g \) opens upward and has its vertex above \( 4 \), then B is true.**
- If \( g \) opens downward, then statements C and D refer to maximum values that may not have a valid comparison.
So, based on typical expectations without specific details of \( g \), the safest assumption is that statement A or B may be true depending on the exact nature of \( g \); if \( g \) opens upward and has a minimum greater than \( 4\), then B will be correct.
In summary:
- **If no additional information is available about function \( g \)**, we can conclude the accurate answer is contingent upon its characteristics and specifically its vertex value in comparison to \( 4\).