Question

A tunnel is in the shape of a parabola.if the tunnel is 40 feet wide and has a maximum height of 12 feet. write the equation of the quadratic function that represents the tunnel(let the axis of symmetry be the y-axis)​

Answer 1

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Answer:

y = -0.03x² +12

Explanation:

For "tunnel" or "arch" or "bridge" problems, I like to start with the expression ...

y = 1 - x²

It has a height of 1 and intersects the x-axis at ±1. This can be scaled to give the appropriate height and x-intercepts.

We want the x-intercepts to be ±20, so we can scale this horizontally by a factor of 20:

y = 1 -(x/20)²

We want the height to be 12, so we can scale it vertically by a factor of 12:

y = 12(1 -(x/20)²

y = 12 -12(x²/400)

y = -0.03x² +12