Question

A particle is moving along a projectile path at an initial height of 80 feet with an initial speed of 112 feet per second. This can be represented by the function H(t) = −16t2 + 112t + 80. What is the maximum height of the particle?

196 feet
276 feet
392 feet
472 feet

Answer 1

thank you!

Answer 2

no problem

Answer 3

Hey please no direct answers, its against the rules. If you want to help then help them work towards the answer, they won't learn if you just give it :c

Answer 4

assuming you haven't learned derivatives yet, you could graph to find the maximum, or convert to vertex form

to find vertex form manually, complete the square:

H(t) = −16t^2 + 112t + 80

subtracting 80 from both sides to isolate the t / t^2 terms

−16t^2 + 112t = -80

now, take the t-term coefficient (112), divide by 2, square the result. add this to both sides. that way, you'll get a perfect square on the left side you can factor.

after full factorization, re-arrange to the form a(t-h)^2 + k = 0. (h,k) will be your vertex so your k-value will be your max height.