How Does the Quadratic Function Model Smooth Transitions in Highway Design?

[lionely]

Homework Statement

In highway design, for civil engineers the quadratic function y= ax^2+bx +c is called the transition curve, because its properties provide a smooth transition between peaks and valleys. A road with an initial gradient of 3% can be represented by the formula y=ax^2+0.3x+c , where y is the elevation and x is the distance along the curve. Suppose the elevation of the road is 1105 feet at points 200 feet and 1000 feet along the curve. Find the equation of the transition curve.


Is this a theory of quadractic equation problem? Where I should use the roots and find the new equation?

 

[SammyS]

Homework Statement

In highway design, for civil engineers the quadratic function y= ax^2+bx +c is called the transition curve, because its properties provide a smooth transition between peaks and valleys. A road with an initial gradient of 3% can be represented by the formula y=ax^2+0.3x+c , where y is the elevation and x is the distance along the curve. Suppose the elevation of the road is 1105 feet at points 200 feet and 1000 feet along the curve. Find the equation of the transition curve.

Is this a theory of quadratic equation problem? Where I should use the roots and find the new equation?

Simply plug-in x=200 and y=1105 into y=ax^2+0.3x+c to get one equation.

Plug-in x=1000 and y=1105 into y=ax^2+0.3x+c to get another equation.

You now have two equations in two unknowns. solve them for a and c

 

[lionely]

Sigh really? =/

 

[Ray Vickson]

Sigh really? =/

Why "sigh"? You have two simple linear equations for a and c, and solving them is easy.

 

[lionely]

I said sigh because I didn't realize it was that easy. :(

 

[MostlyHarmless]

Occam's razor!