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Exam-Style Question on Quadratic ModelsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 106. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.
The cross-section of a fish pond is drawn on a set of axes shown below. The edge is modelled by \(y=ax^2+c\) and the cross section is the same for the whole of its length. The curve touches the x-axis at the origin.
Point A has coordinates (-9,5.4) and point B has coordinates (9,5.4).
(a) Find the value of \(c\).
(b) Find the value of \(a\).
(c) Hence write down the equation of the quadratic function which models the edge of the fish pond.
(d) Calculate the value of \(y\) when \(x\)=7.2m.
(e) State what the value of \(x\) and the value of \(y\) represent for this fish pond.
(f) Find the value of \(x\) when the height of water in the pond is 2m.
The pond is filled so that the cross-sectional area of the water is 22.9m2. The pond has a length of 8m.
(g) Calculate the volume of water in the pond.
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