The height in feet of the curved arch support for a bridge can be modeled by f(x) = -0.0009x2 + 1.24x + 1.65. You are standing on a platform 2 feet above the maximum height ofthe arch. If you bungee from this point, and your bungee will stretch to 420 feet before retracting;are you safe to jump?
A) Yes you are totally safe!
B) No, you will hit the ground before your bungee retracts

SHow steps please!

A) Yes you are totally safe

Step-by-step explanation:

The function that models the height of the curved arch in feet, f(x) = -0.0009·x² + 1.24·x + 1.65

The height of the platform = 2 feet + The maximum height of the arch

The amount of stretch of the bungee before retracting = 420 feet

The vertex of the parabola is the point x = (-b/2·a), from which we get;

At the maximum height of the arch, x = -1.24/(2 × -0.0009) = 6,200/9 =  688.

The maximum height of the arch = f(688.), therefore, we have;

f(688.) = -0.0009×(688.)² + 1.24 × (688.) + 1.65 = 428.76

The maximum height of the arch = 428.76 feet

The height of the platform above the ground = 2 ft. + 428.76 ft. = 430.76 ft.

Therefore;

The height of the platform above the ground = 430.76 feet > The amount the bungee will stretch before retracting = 420 ft.

430.76 ft, > 420 ft.

Therefore, the jumper is totally safe.

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