1. ## Parabola word problem about a suspension bridge

The two towers on either end will be 50 feet high and 300 feet apart. The two supporting cables are connected at the top of the towers and hang in a curve that is a parabola. There are vertical cables that connect the walkway to the supporting cables. These cables will be connected every 15 feet from the walkway up to the supporting cables. At the center of the bridge, the parabola will be 5 feet above the walkway.
The cable material can be purchased from Company A for $52.75 per 10 feet with a shipping charge of$300.00 for the entire order or from Company B for $432.90 per 100 feet with a shipping charge of$350.00 for the entire order. You must purchase full 10-foot cables from Company A or 100-foot cables from Company B. The cables can be cut or welded together.

Questions:
1.Write an equation for the parabola that represents each of the support cables.

2. Determine the number of vertical cables needed.

3. Determine the length of each of the vertical cables.

4. How much does it cost to purchase the needed materials from each company?

2. Originally Posted by iluvpigs1991
The two towers on either end will be 50 feet high and 300 feet apart. The two supporting cables are connected at the top of the towers and hang in a curve that is a parabola. There are vertical cables that connect the walkway to the supporting cables. These cables will be connected every 15 feet from the walkway up to the supporting cables. At the center of the bridge, the parabola will be 5 feet above the walkway.
The cable material can be purchased from Company A for $52.75 per 10 feet with a shipping charge of$300.00 for the entire order or from Company B for $432.90 per 100 feet with a shipping charge of$350.00 for the entire order. You must purchase full 10-foot cables from Company A or 100-foot cables from Company B. The cables can be cut or welded together.

Questions:
1.Write an equation for the parabola that represents each of the support cables.

2. Determine the number of vertical cables needed.

3. Determine the length of each of the vertical cables.

4. How much does it cost to purchase the needed materials from each company?
here's a sketch of the function to get you started ...

the parabola with an vertex at $(0,5)$
is $(x)^2 = 4a(y-5)$ with it opening upwards (with the parabola 5 ft from the base and this assuming the tower height is also from the base

with a point of $(150,50)$ we can find the value of $a$

$(150)^2 = 4a(50-5) \Rightarrow a = 125$

so then

$x^2 = 4\left(125\right)(y-5)$ or $x^2=500(y-5)$

to graph this we solve for $y$ in terms of $x$
$y = \frac{x^2}{500}+5$

in order to get the lenghts of the cable supports just plug the x values to get y for the height