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).

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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).

Mathematics
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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
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
so the answer is A

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Thank you so much! ^.^
no prblem :)

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