Question

The height of the tunnel at the center is 35ft, and the vertical clearance must be 21 ft at a point of 8ft from the center. Find an equation for the parabola.

INCLUDE WORK.

Answer 1

y=-0.215x^2+35

Step by Step:

Let,
`h=0`,
`k=35`,
`x=8`,
`y=21`

We know that, the general equation of the parabola.

`y-k = a(x-h)^2`

`\Rightarrow y=a(x-h)^2+k .........(i)`

Substitute the value of
`h, k, x, y` in equation
`(i)` and find the value of
`a.`

`21=a(8-0)^2+35`

`\Rightarrow 21=a* 8^2+35`

`\Rightarrow 21=64a+35`

`\Rightarrow 64a=21-35`

`\Rightarrow 64a=-14`

`\Rightarrow a=(-14)/(65)`

`\Rightarrow a=-0.215`

Hence, the equation of the parabola is:

`y=-0.215x^2+35`