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**Topic**

In a project, a parabolic entrance gate is built (illustrated in Figure 13) so that the distance between the two legs of the gate BC is 9 m. From a point M on the gate body, one can measure the distance to the ground is MK = 1.6 m and the distance from K to the foot of the nearest gate is BK = 0.5 m. Calculate the height of the gate in meters (round to tenths)

**Solution method – See details**

Attach the coordinate system to the parabolic gate, make a parabolic equation representing the gate

**Detailed explanation**

Take the coordinate system \(Oxy\) such that the position of point B coincides with the origin O, the axis \(Ox\) lies on the line connecting the two gates, C lies on the ray \(Ox\) (units on the axes in meters)

Then the total input is part of the graph of the function \(y = \frac{{ – 32}}{{85}}{x^2} + \frac{{288}}{{85}}x\” )

The vertex of the graph of the above function has a coordinate of 7.6

So the height of the gate is 7.6 m.

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