Question

Can someone explain this? Will medal and fan!

The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).

Answer 1

f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground

Answer 2

by checking the options u can clearly see that - 4t^2 -8t+7 = 4(t-1)^2 +3

and now you need to find the minimum height attained so for this u jst need to differentiate f(t) and equal it to zero and then u'll get the value of time(t) at which the height is min.

so differentiating f(t)= 4t^2 -8t +7

differentiating with respect to t and equal it to 0

u get

8t - 8 =0
t=1sec

plug this value of t in f(t)

u get 4t^2 - 8t +7
4(1)^2 -8(1)+7
=3

Answer 3

so the answer is A

Answer 4

Thank you so much! ^.^

Answer 5

no prblem :)