Close to the surface, Earth objects fall with a constant acceleration approximately equal to -32 ft/s². The height of any object launched from the surface of the earth can be approximated using the function, h(t) = v₀t − 16t², where t is time in seconds after the launch and v₀ is the initial vertical launch velocity.
Find the v₀ you will use for your project by multiplying the number of letters in your first name by 32 ft/s. Use this initial velocity throughout this project. v₀ = 128 ft/s
The function f(t) = v₀t − 16.087t² models the height of an object launched from the surface Earth more precisely than h(t) from part 1, but completing the square and factoring are impractical for f(t).
10.An object is launched from ground level with the same initial velocity as in parts 1 and 2. Write a function, f(t), for the height of the object at time t seconds after launch.
11.Show how you can use (-b/2a, f(-b/2a)) to find both coordinates of the vertex of f(t), rounding your final coordinates to the nearest tenth of a second and tenth of a foot.
12.Show how you can use the quadratic formula to find the duration of the flight to the nearest hundredth of a second.
Conclusion
13.Write a conclusion explaining the strengths and weaknesses of each form of a quadratic function, h(t) = a(t - h)² + k, factored form and f(t) = at² + bt + c.