Quadratic Functions, Equations and Inequalities - Quadratic Inequalities
Quadratic Functions, Equations and Inequalities - Quadratic Inequalities
TGM Original Questions
An engineer is designing a parabolic suspension bridge. The bridge's cable follows a parabolic shape and is represented by the quadratic equation \(y=0.01{{x}^{2}}-0.4x+10\), where \(y\) (in meters) is the height of the cable above the bridge deck, and \(x\) (in meters) is the horizontal distance from the left end of the bridge as shown in the diagram below.
- Determine the height of the lowest point of the cable, and how far from the ends of the bridge it occurs.
- Find the height of the cable when \(x=15\).
- Find the range of values of \(x\) for which the cable is at least \(9\) metres above the bridge deck.
- Determine the length of the bridge deck that lies directly beneath the bridge cable.
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Answer:(a) Lowest point \(= 6\) m at \(20\) m from the ends of the bridge (b) Height of cable \(=6.25\) m when \(x = 15\) m (c) \(0\le x\le2.68\) or \(37.3\le x\le40\) (3 s.f.) (d) Length of bridge deck \(= 20 \text{ m} \times 2 = 40\) m
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