B. f(t) = 4(t - 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C. f(t) = 4(t - 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D. f(t) = 4(t - 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
The function f(t)can be written in the vertex form as: C. f(t) = 4(t - 1)² + 2; the minimum height of the roller coaster is 2 meters from the ground.
Since the leading coefficient in the given function f(t) is positive 4, the parabola will open upward and at the vertex. Also, the value of the function f(t) would be minimum.
Evaluating the function by applying completing the square, we have:
f(t) = 4t² - 8t + 6
f(t) = 4(t² - 2t) + 6
f(t) = 4(t² - (2 × t × 1) + 1² - 1²) + 6
f(t) = 4(t² - (2 × t × 1) + 1² - 1) + 6
f(t) = 4(t² - 2t + 1²) - 4 + 6
f(t) = 4(t² - 2t + 1²) + 2
f(t) = 4(t - 1)² + 2.
Therefore, the vertex of f(t) will be at (1, 2) and the minimum height of the roller coaster is 2 meters from the ground.
Read more on vertex here: brainly.com/question/1561064
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