Find accurate and reliable answers to your questions on IDNLearn.com. Our platform is designed to provide accurate and comprehensive answers to any questions you may have.
Sagot :
To find a quadratic model for the given data points using quadratic regression, follow these steps:
1. List the Data Points:
- Speed (x): 10, 20, 30, 40, 50, 60, 70
- Stopping Distance (y): 12.5, 36.0, 69.5, 114.0, 169.5, 249.0, 325.5
2. Formulate a Quadratic Model:
- The general form of a quadratic model is [tex]\( y = ax^2 + bx + c \)[/tex].
3. Determine the Coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
- Using quadratic regression methods, we can determine the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
- After applying quadratic regression to the given data points and rounding the coefficients to the nearest hundredths place, we get:
- [tex]\( a = 0.06 \)[/tex]
- [tex]\( b = 0.31 \)[/tex]
- [tex]\( c = 4.0 \)[/tex]
4. Construct the Model Equation:
- Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the quadratic model [tex]\( y = ax^2 + bx + c \)[/tex]:
[tex]\[ y = 0.06x^2 + 0.31x + 4.0 \][/tex]
5. Compare with Given Options:
- Option a: [tex]\( y = 0.06x^2 + 0.31x + 4 \)[/tex]
- Option b: [tex]\( y = -4.03x^2 + 0.32x + 8.19 \)[/tex]
- Option c: [tex]\( y = 0.06x^2 - 0.31x - 4 \)[/tex]
- Option d: [tex]\( y = 4.03x^2 - 0.32x - 8.19 \)[/tex]
6. Identify Correct Option:
- The model we constructed, [tex]\( y = 0.06x^2 + 0.31x + 4.0 \)[/tex], matches Option a.
Therefore, the correct answer is:
a. [tex]\( y = 0.06x^2 + 0.31x + 4 \)[/tex].
1. List the Data Points:
- Speed (x): 10, 20, 30, 40, 50, 60, 70
- Stopping Distance (y): 12.5, 36.0, 69.5, 114.0, 169.5, 249.0, 325.5
2. Formulate a Quadratic Model:
- The general form of a quadratic model is [tex]\( y = ax^2 + bx + c \)[/tex].
3. Determine the Coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
- Using quadratic regression methods, we can determine the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
- After applying quadratic regression to the given data points and rounding the coefficients to the nearest hundredths place, we get:
- [tex]\( a = 0.06 \)[/tex]
- [tex]\( b = 0.31 \)[/tex]
- [tex]\( c = 4.0 \)[/tex]
4. Construct the Model Equation:
- Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the quadratic model [tex]\( y = ax^2 + bx + c \)[/tex]:
[tex]\[ y = 0.06x^2 + 0.31x + 4.0 \][/tex]
5. Compare with Given Options:
- Option a: [tex]\( y = 0.06x^2 + 0.31x + 4 \)[/tex]
- Option b: [tex]\( y = -4.03x^2 + 0.32x + 8.19 \)[/tex]
- Option c: [tex]\( y = 0.06x^2 - 0.31x - 4 \)[/tex]
- Option d: [tex]\( y = 4.03x^2 - 0.32x - 8.19 \)[/tex]
6. Identify Correct Option:
- The model we constructed, [tex]\( y = 0.06x^2 + 0.31x + 4.0 \)[/tex], matches Option a.
Therefore, the correct answer is:
a. [tex]\( y = 0.06x^2 + 0.31x + 4 \)[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.