B2. Lara has a garden hose, which she held 1 meter above the ground, creating a water jet in the shape of a parabolic curve $y=-2 x^{2}+4 x+1$, as shown in the figure.

A. How high does the water jet reach?

B. Calculate how far away the water jet will land on the ground.

C. Through the hose, 18 liters of water flow every minute. In what time would Lara fill a 1.2 m high plastic barrel in the shape of a cylinder, whose base radius is 30 cm?

![](https://cdn.mathpix.com/cropped/2024_06_07_debf03cdc366cb9b1122g-08.jpg?height=588&width=596&top_left_y=177&top_left_x=1324)
B2. From the graph, it is evident that the water jet reaches a height of three meters.

The water jet falls on the ground $2.22 \mathrm{~m}$ away, which is the solution to the equation $-2 x^{2}+4 x+1=0 ; x_{1}=2.2$ and $x_{2}=-0.2$ (an inappropriate solution).

The volume of the tank is $V=\pi r^{2} v=\pi \cdot(3 \mathrm{dm})^{2} \cdot 12 \mathrm{dm}=339.12 \mathrm{dm}^{3}=339.12 \ell$. The tank fills in $339.12 \ell: 18 \frac{\ell}{\text { min }} \approx 19 \mathrm{~min}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_debf03cdc366cb9b1122g-13.jpg?height=57&width=1562&top_left_y=1179&top_left_x=293)

![](https://cdn.mathpix.com/cropped/2024_06_07_debf03cdc366cb9b1122g-13.jpg?height=57&width=1545&top_left_y=1251&top_left_x=307)

C. The calculated volume of the tank $339.12 \ell$.............................................. 2 t

![](https://cdn.mathpix.com/cropped/2024_06_07_debf03cdc366cb9b1122g-13.jpg?height=63&width=1488&top_left_y=1368&top_left_x=364)