The quadratic function which describes the shape of the tunnel exists [tex]$y=\frac{-8}{9}(x-3)(x+3)$[/tex].
A quadratic function is one of the form [tex]$f(x) = ax^{2} + bx + c[/tex], where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function exists a curve named a parabola.
Consider the figure above,
The parabola cuts x-axis at -3 and 3 .
We have conjugate (x-3) and (x+3)
Then, y = a(x+3)(x-3)
[tex]${data-answer}amp;=a\left(x^{2}-9\right)[/tex]
Parabola passes through (0,8)
So, [tex]${data-answer}amp;y=a\left(x^{2}-9\right) \\[/tex]
[tex]${data-answer}amp;8=a\left(0^{2}-9\right) \\[/tex]
[tex]${data-answer}amp;-9 a=8 \\[/tex]
[tex]${data-answer}amp;a=\frac{-8}{9}[/tex]
The quadratic function which describes the shape of the tunnel exists [tex]$y=\frac{-8}{9}(x-3)(x+3)$[/tex].
To learn more about quadratic function
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