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

Answer:

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 $a.$

  $21=a(8-0)^2+35$

$\Rightarrow 21=a\times 8^2+35$

$\Rightarrow 21=64a+35$

$\Rightarrow 64a=21-35$

$\Rightarrow 64a=-14$

$\Rightarrow a=\frac{-14}{65}$

$\Rightarrow a=-0.215$

Hence, the equation of the parabola is:

$y=-0.215x^2+35$