A new theme park is designing a rollercoaster. The height of the rollercoaster above the ground is modelled by a polynomial function, \(h(x)\), where \(x\) is the horizontal distance from the starting point of the rollercoaster, and \(h(x)\) is the height in meters. The section of the rollercoaster between \(x=0\) and \(x=8\) is modelled by a quartic polynomial. It is known that the rollercoaster starts at ground level, has a local minimum at \((2, -4)\), and returns to ground level at \(x=8\). Additionally, there is a point of inflection at \(x=5\).
a. Deduce the form of the quartic polynomial \(h(x)\), expressing it in terms of unknown coefficients. Justify your reasoning based on the given information.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Polynomial Equation Solutions. It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of polynomial equations with real coefficients of degree $n$ having up to $n$ real solutions, including numerical solutions
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