Let's Practice
Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct--if you don't, review that part of the lesson.
Does the polynomial equation \( y = –0.11x^2 + 4.95x + 12.69 \), have an absolute maximum or a relative maximum?
- relative
- absolute
Even degree polynomials can have up to n – 1 relative extrema and 0 or an even number of absolute extrema.
Even degree polynomials can have up to n – 1 relative extrema and 0 or an even number of absolute extrema.
Find the absolute maximum of the polynomial equation \( y = –0.11x^2 + 4.95x+ 12.69 \).
- (14, 60.33)
- (47.432, 0)
- (0, 12.69)
- (22.5, 68.37)
Use a graphing utility to view the curve and interpret what you see.
Use a graphing utility to view the curve and interpret what you see.
Use a graphing utility to view the curve and interpret what you see.
Use a graphing utility to view the curve and interpret what you see.
These data represent the height of a ball, in feet, that is thrown into the air. Describe the finite differences of these data.
Time (sec)
0
1
2
3
4
5
6
7
Height (feet)
6
102
166
198
198
166
102
6
| Time (sec) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Height (feet) | 6 | 102 | 166 | 198 | 198 | 166 | 102 | 6 |
- The first-order differences are non-zero and constant.
- The second-order differences are non-zero and constant.
- The third-order differences are non-zero and constant.
- The fourth-order differences are non-zero and constant.
If a polynomial function has a degree of n, then the nth-order differences of that function will be nonzero and constant.
If a polynomial function has a degree of n, then the nth-order differences of that function will be nonzero and constant.
If a polynomial function has a degree of n, then the nth-order differences of that function will be nonzero and constant.
If a polynomial function has a degree of n, then the nth-order differences of that function will be nonzero and constant.
These data represent the height of a ball, in feet, that is thrown into the air. What polynomial function models these data if H(t) represents the height of the ball and t is the time in seconds?
Time (sec)
0
1
2
3
4
5
6
7
Height (feet)
6
102
166
198
198
166
102
6
| Time (sec) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Height (feet) | 6 | 102 | 166 | 198 | 198 | 166 | 102 | 6 |
- \( H(t) = –16t + 6 \)
- \( H(t) = –16t^3 + 4t^2 + 123t + 6 \)
- \( H(t) = –16t^2 + 112t + 6 \)
- \( H(t) = –16t^4 + 112t^2 + 6 \)
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant.
These data represent the height of a ball, in feet, that is thrown into the air. What is the ball’s maximum height?
Time (sec)
0
1
2
3
4
5
6
7
Height (feet)
6
102
166
198
198
166
102
6
| Time (sec) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Height (feet) | 6 | 102 | 166 | 198 | 198 | 166 | 102 | 6 |
- 198 feet
- 202 feet
- 247 feet
- 276 feet
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant. Then use a graphing utility to see a picture of the curve and find the maximum value.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant. Then use a graphing utility to see a picture of the curve and find the maximum value.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant. Then use a graphing utility to see a picture of the curve and find the maximum value.
Use your technology to find the equation of the line of best fit. Remember that the second-order differences were non-zero and constant. Then use a graphing utility to see a picture of the curve and find the maximum value.
Summary
Questions answered correctly:
Questions answered incorrectly:
