2.42 - Explain why the second differences of curve elevations are equal for a parabolic curve.
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Practice Questions
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Define a parabolic curve.
💡 Hint: Remember the equation form y = ax² + bx + c.
What are second differences in terms of elevation?
💡 Hint: Think about how you find the differences in a series of values.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What type of equation defines a parabolic curve?
💡 Hint: Recall the form y = ax² + bx + c.
Are the second differences of a parabolic curve equal?
💡 Hint: Think about the mathematical characteristics of parabolas.
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Challenge Problems
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Given a parabolic equation y = 2x² + 3x + 4, calculate the second differences for x = 0, 1, 2, and 3.
💡 Hint: Focus on calculating successive differences at equal intervals.
If a road is designed with a parabolic vertical curve connecting a 5% to a 1% gradient, what elevation modeling will ensure second differences remain equal?
💡 Hint: Map how gradients could be approached using quadratic functions.
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