1. ## Finding a function to model a road arch.

A wildlife corridor must be disnged to arch over a major highway. The arch over the highway is to be constructed in the shape fo a parabola. The highway is 8 m wide and will be centered under the parabolic arch. The arch must span a total width of 12 m at its base. The arch must provide a minumum cledarance of 4 m over the highway.

A) Describe the type of function that will be used to model the roadway arch dimensions.

B) Sketch the parabolic arch and highway, laeling all relevant dimensions

2. Look here.

3. I dont understand how to determine what function it is?

4. It's a parabola. Parabolas have the form (in this case, since you know the parabola is going to open down)

$\displaystyle y=-a x^{2}+bx+c$,

where $\displaystyle a>0$.

Now, you need to plug in various values of $\displaystyle y$ and $\displaystyle x$ in order to find $\displaystyle a$, $\displaystyle b$, and $\displaystyle c$. Does that make sense?

5. how would i determine the y and x values? would they be the 8, 12, and 4?

6. You need to plug in various y and x values that you know are on the parabola. For example, you're told that the arch must span 12 m at the base. If you center the parabola on the y axis, then you know that the point (6,0) must be on the parabola. What other points do you know must be on the parabola?