# 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 22.9m2. The pond has a length of 8m.

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

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