4B. A parabolic bridge needs to be built over a river that is $30 \mathrm{~m}$ wide, with pillars spaced $5 \mathrm{~m}$ apart. The height of the central pillar is $7.5 \mathrm{~m}$.

What are the heights of the other pillars?
Solution. We place the bridge in a coordinate system as shown in the diagram. Then the equation of the parabola is $y=a x^{2}+b$ and since it passes through the points $(0 ; 7.5)$ and $(15,0)$, we get $b=7.5$ and $a=-\frac{1}{30}$. The heights of the other pillars are

![](https://cdn.mathpix.com/cropped/2024_06_05_5cbf21d72fe8685988dag-12.jpg?height=344&width=762&top_left_y=1222&top_left_x=720)
$h_{1}=-\frac{1}{30} 5^{2}+7.5=\frac{20}{3}$ and $h_{2}=-\frac{1}{30} 10^{2}+7.5=\frac{25}{6}$.