Question

An arch is in the shape of a parabola. It has a span of 96 feet and a maximum height of 8 feet.Find the equation of the parabola. ______________Determine the distance from the center at which the height is 2 feet. ___________

Answer 1

We know the equation of a parabola can be written as

y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros

y = a ( x - 48) ( x - -48)

y = a ( x-48) (x+48)

Now when x = 0 y = 8

8 = a ( 0-48) ( 0+48)

8 = a (-2304)

-8/2304 = a

-1/288 = a

y = -1/288 ( x-48) (x+48)

This is the equation for the parabola

Now let y = 2

2 = -1/288 ( x-48) (x+48)

Multiply each side by -288

-576 = (x-48)(x+48)

FOIL

-576 = x^2- 2304

ADD 2304 to each side

1728=x^2

Take the square root of each side

24 sqrt(3) = x

24 sqrt(3) ft

41.569 ft