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:

y=-0.215x^2+35

Step by Step:

Let, [tex]h=0[/tex],  [tex]k=35[/tex], [tex]x=8[/tex], [tex]y=21[/tex]

We know that, the general equation of the parabola.

   [tex]y-k = a(x-h)^2[/tex]

[tex]\Rightarrow y=a(x-h)^2+k .........(i)[/tex]

Substitute the  value of [tex]h, k, x, y[/tex] in equation [tex](i)[/tex] and find the value of [tex]a.[/tex]

  [tex]21=a(8-0)^2+35[/tex]

[tex]\Rightarrow 21=a\times 8^2+35[/tex]

[tex]\Rightarrow 21=64a+35[/tex]

[tex]\Rightarrow 64a=21-35[/tex]

[tex]\Rightarrow 64a=-14[/tex]

[tex]\Rightarrow a=\frac{-14}{65}[/tex]

[tex]\Rightarrow a=-0.215[/tex]

Hence, the equation of the parabola is:

[tex]y=-0.215x^2+35[/tex]

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