Question

The parabolic arch of a bridge over a one-way road can be described by the equation y = -x^2 + 6, where x and y ar emeasured in metres. A transpor truck is 3m wide and 3.5m high. What is the maximum clearance of the truck's top corners if it passes under the bridge?

Answer 1

So check the picture below

if we check the solutions or zeros for the equation, we get $\bf y=-x^2+6\implies 0=-x^2+6\implies x=\pm \sqrt{6}$

and as you can see in the picture, the value of "x" when y = 3.5, or the height of the truck is  $\bf y=-x^2+6\implies 3.5=-x^2+6\implies x=\pm \sqrt{2.5}$

the truck, ends up with a clearance of $\bf \sqrt{2.5}-1.5$ on either side, so, the maximum clearance, the truck can have, those two clearances added together, $\bf 2(\sqrt{2.5}-1.5)$