Question

The function f(t) = 4t2 − 8t + 8 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).

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

Answer 1

The function f(t) = 4t2 − 8t + 8 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. The f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, is f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground. The answer is letter D.

Answer 2

Answer:
`f(t)=4(t-1)^2+4`; the minimum height of the roller coaster is 4 meters from the ground.

Explanation:

Given: function
`f(t)=4t^2-8t+8` shows the height from the ground f(t), in meters, of a roller coaster car at different times t.

In vertex form

`f(t)=4t^2-8t+8\\\Rightarrow\ f(t)=4(t^2-2t)+8\\\Rightarrow\ f(t)=4(t^2-2t+1-1)+8\\\Rightarrow\ f(t)=4(t^2-2t+1)-4+8\\\Rightarrow\ f(t)=4(t-1)^2+4.......[as\ t^2-2t+1=(t-1)^2]`

For , the minimum height put t=1, we get

`f(t)=4(1-1)^2+4\\\Rightarrow\ f(1)=0+4\\\Rightarrow\ f(1)=4\ meters`

∴ The minimum height of the roller coaster is 4 meters from the ground= 4 meters.