



 
Hi Sue, I drew a diagram of what you described with the measurements in metres. I introduced an X and Y axis with the road on the Xaxis and the Yaxis passing through the vertex of the parabola. Since this is a parabola that opens downward and the vertex is above the Xaxis I can write its equation y = ax^{2} + b where a and b are positive. Do you see why a and b must be positive? Since there must be at least a 3 m clearance over all areas of the road when x = 7, y must be at least 3. In order to not make the bridge higher than it needs to be let y = 3 when x = 7. Thus
Solve this equation for b and substitute into y = ax^{2} + b. This will give you a model with a still to be determined from other considerations. For example how high is the bridge at its highest point? What is a if this height is 5 metres? What if it's only 4 metres? Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 