# Math Help - Quadratic equation word problem

1. ## Quadratic equation word problem

I have this question:
A concrete bridge over a river has an underside in the shape of a parabolic arch. At the water level, the arch is 30m wide. It has a maximum height of 10m above the water. The minimum vertical thickness of the concrete is 1.5m.

a)Write an algebraic relation that represents the shape of the arch.
b)What is the vertical thickness of the concrete 3m from the centre of the arch?
c) if the water rises 2m, how wide will the arch be at this new level?

So far I think:
a) max=-(x-0)^2+10

2. Originally Posted by Squirrels
I have this question:
A concrete bridge over a river has an underside in the shape of a parabolic arch. At the water level, the arch is 30m wide. It has a maximum height of 10m above the water. The minimum vertical thickness of the concrete is 1.5m.

a)Write an algebraic relation that represents the shape of the arch.
b)What is the vertical thickness of the concrete 3m from the centre of the arch?
c) if the water rises 2m, how wide will the arch be at this new level?

So far I think:
a) max=-(x-0)^2+10
1. Define a coordinate system: The x-axis is at water level. the y-axis passes through the vertex of the parabola.

2. Then you know:
$\left\{\begin{array}{l}p(x)=ax^2+b \\ p(0)=10 \\ p(15)=0\end{array}\right.$ ........Solve for a and b. I've got $a = -\dfrac2{45}\ ,\ b = 10$

3. The street level over the bridge is described by y = 11.5.
Therefore the thickness of the concrete could be calculated by

$t = 11.5 - p(3)$

4. If the water has risen by 2 m the water level is described by y = 2.

Plug in p(x) = 2 and solve for x.