# Thread: [SOLVED] How to solve this word problem ?

1. ## [SOLVED] How to solve this word problem ?

Bridge is build in a shape of a parabolic arch and its span is 140 feet.
The height of the arch a distance of 50 feet from the center is to be 12 feet.
Whats the height of the arch at its center.

* Round to nearest tenth place if necessary.

#1 * Equation of the parabola in standard form.
#2 * Height at center.

How exactly is one suppose to solve this problem?

2. Standard form:$\displaystyle y=a(x-h)^2+k$

Assuming a is negative for the bridge and center of bridge is half the 140 ft span: $\displaystyle y=-a(x-70)^2+k$

$\displaystyle 12=-a(20-70)^2+k$ 50 ft from center span is 12 ft high
$\displaystyle 12=-2500a+k$

And
$\displaystyle 0=-a(140-70)^2+k$ at 140 ft the arch is back on the ground
$\displaystyle 0=-4900a+k$

Solving the two equations you find $\displaystyle a=\frac{1}{200}~=.005 ~and~ k=\frac{49}{2}~=24.5$

Equation is then:
#1) $\displaystyle y=-\frac{1}{200}(x-70)^2+\frac{49}{2}$
#2) Looking at k, the height at the center, is 24.5 ft.

3. its suppose to be i guess in the p4 form

4. Originally Posted by xterminal01
its suppose to be i guess in the p4 form
Who or what is a "p4" form?

-Dan