Question
Which quadratic function has a range that can be described as y≤10.5
?(1 point)
Responses
f(x)=6(x+4)2+10.5
f left parenthesis x right parenthesis equals 6 left parenthesis x plus 4 right parenthesis squared plus 10.5
f(x)=−6(x−10.5)2+4
f left parenthesis x right parenthesis equals negative 6 left parenthesis x minus 10.5 right parenthesis squared plus 4
f(x)=10.5(x−4)2−6
f left parenthesis x right parenthesis equals 10.5 left parenthesis x minus 4 right parenthesis squared minus 6
f(x)=−6(x+4)2+10.5
f left parenthesis x right parenthesis equals negative 6 left parenthesis x plus 4 right parenthesis squared plus 10.5
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?(1 point)
Responses
f(x)=6(x+4)2+10.5
f left parenthesis x right parenthesis equals 6 left parenthesis x plus 4 right parenthesis squared plus 10.5
f(x)=−6(x−10.5)2+4
f left parenthesis x right parenthesis equals negative 6 left parenthesis x minus 10.5 right parenthesis squared plus 4
f(x)=10.5(x−4)2−6
f left parenthesis x right parenthesis equals 10.5 left parenthesis x minus 4 right parenthesis squared minus 6
f(x)=−6(x+4)2+10.5
f left parenthesis x right parenthesis equals negative 6 left parenthesis x plus 4 right parenthesis squared plus 10.5
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page 14 of 14
Answers
Answered by
GPT-4o mini
To determine which quadratic function has a range described by \( y \leq 10.5 \), we need to identify functions that open downward (since a downward-opening parabola has a maximum value).
Let's analyze each of the functions:
1. **\( f(x) = 6(x+4)^2 + 10.5 \)**
This is a quadratic function that opens upward (the coefficient of \( (x+4)^2 \) is positive), so its range is \( y \geq 10.5 \).
2. **\( f(x) = -6(x-10.5)^2 + 4 \)**
This is a downward-opening parabola (the coefficient of \( (x-10.5)^2 \) is negative), and its maximum value is \( 4 \). Therefore, its range is \( y \leq 4 \).
3. **\( f(x) = 10.5(x-4)^2 - 6 \)**
This is another upward-opening parabola, so its range will be \( y \geq -6 \).
4. **\( f(x) = -6(x+4)^2 + 10.5 \)**
This is a downward-opening parabola, and its maximum value is \( 10.5 \). Therefore, its range is \( y \leq 10.5 \).
The function that has a range described by \( y \leq 10.5 \) is:
**\( f(x) = -6(x+4)^2 + 10.5 \)**
Let's analyze each of the functions:
1. **\( f(x) = 6(x+4)^2 + 10.5 \)**
This is a quadratic function that opens upward (the coefficient of \( (x+4)^2 \) is positive), so its range is \( y \geq 10.5 \).
2. **\( f(x) = -6(x-10.5)^2 + 4 \)**
This is a downward-opening parabola (the coefficient of \( (x-10.5)^2 \) is negative), and its maximum value is \( 4 \). Therefore, its range is \( y \leq 4 \).
3. **\( f(x) = 10.5(x-4)^2 - 6 \)**
This is another upward-opening parabola, so its range will be \( y \geq -6 \).
4. **\( f(x) = -6(x+4)^2 + 10.5 \)**
This is a downward-opening parabola, and its maximum value is \( 10.5 \). Therefore, its range is \( y \leq 10.5 \).
The function that has a range described by \( y \leq 10.5 \) is:
**\( f(x) = -6(x+4)^2 + 10.5 \)**