## Exam-Style Questions on Functions Quadratic Models Integration## Problems on Functions Quadratic Models Integration adapted from questions set in previous exams. |

## 1. | IB Studies |

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 2.7m.

The pond is filled to a maximum depth of 2.7m and the the cross-sectional area of the water is 22.9m^{2}. The pond has a length of 8m.

(g) Calculate the volume of water in the pond.

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