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f(x) = 2x2 – 8x + 8, The height of a section of a roller-coaster ride is given by the equation h = for 0 < x < 3. 4 0.5 1.0 1.5 2.0 2.5 3.0 Part 1. The planners decide that the following section, for 3 < x < 5, should take the shape of a parabola, with the height given by the equation h = g(x) = kx² + 16x – 28. (a) Find lim f (x). x→3 ° (b) Find the limit for second section g(x) as x approaches 3. (c) Explain what value of k is required for the two sections of the roller-coaster to fit together. What can you say about the function for the height of the roller-coaster at x = 3. Part 2. From the lowest point on the first section, the slope of the line of sight to each other point on the 2(x – 2)2 (x – 2) - first section is given by the equation h(x) = (a) Does the limit of h(x) as x approaches 2 exist? If so, give the value of the limit. (b) Is the function h(x) continuous at x = 2? Explain why or why not. (c) Does the concept behind the function h(x) make sense at x = = 2, and if so, what does it represent.

f(x) = 2x2 – 8x + 8, The height of a section of a roller-coaster ride is given by the equation h = for 0 < x < 3. 4 0.5 1.0 1.5 2.0 2.5 3.0 Part 1. The planners decide that the following section, for 3 < x < 5, should take the shape of a parabola, with the height given by the equation h = g(x) = kx² + 16x – 28. (a) Find lim f (x). x→3 ° (b) Find the limit for second section g(x) as x approaches 3. (c) Explain what value of k is required for the two sections of the roller-coaster to fit together. What can you say about the function for the height of the roller-coaster at x = 3. Part 2. From the lowest point on the first section, the slope of the line of sight to each other point on the 2(x – 2)2 (x – 2) - first section is given by the equation h(x) = (a) Does the limit of h(x) as x approaches 2 exist? If so, give the value of the limit. (b) Is the function h(x) continuous at x = 2? Explain why or why not. (c) Does the concept behind the function h(x) make sense at x = = 2, and if so, what does it represent.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter10: Quadratic Equations
Section10.5: Graphing Quadratic Equations
Problem 10.108TI: A toy rocket shot upward from the ground at a rate of 208 ft/sec has the quadratic equation of...
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f(x) = 2x2 – 8x + 8, The height of a section of a roller-coaster ride is given by the equation h = for 0 < x < 3. 4 0.5 1.0 1.5 2.0 2.5 3.0 Part 1. The planners decide that the following section, for 3 < x < 5, should take the shape of a parabola, with the height given by the equation h = g(x) = kx² + 16x – 28. (a) Find lim f (x). x→3 ° (b) Find the limit for second section g(x) as x approaches 3. (c) Explain what value of k is required for the two sections of the roller-coaster to fit together. What can you say about the function for the height of the roller-coaster at x = 3. Part 2. From the lowest point on the first section, the slope of the line of sight to each other point on the 2(x – 2)2 (x – 2) - first section is given by the equation h(x) = (a) Does the limit of h(x) as x approaches 2 exist? If so, give the value of the limit. (b) Is the function h(x) continuous at x = 2? Explain why or why not. (c) Does the concept behind the function h(x) make sense at x = = 2, and if so, what does it represent.
Transcribed Image Text:f(x) = 2x2 – 8x + 8, The height of a section of a roller-coaster ride is given by the equation h = for 0 < x < 3. 4 0.5 1.0 1.5 2.0 2.5 3.0 Part 1. The planners decide that the following section, for 3 < x < 5, should take the shape of a parabola, with the height given by the equation h = g(x) = kx² + 16x – 28. (a) Find lim f (x). x→3 ° (b) Find the limit for second section g(x) as x approaches 3. (c) Explain what value of k is required for the two sections of the roller-coaster to fit together. What can you say about the function for the height of the roller-coaster at x = 3. Part 2. From the lowest point on the first section, the slope of the line of sight to each other point on the 2(x – 2)2 (x – 2) - first section is given by the equation h(x) = (a) Does the limit of h(x) as x approaches 2 exist? If so, give the value of the limit. (b) Is the function h(x) continuous at x = 2? Explain why or why not. (c) Does the concept behind the function h(x) make sense at x = = 2, and if so, what does it represent.
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