 Mathematics
5 September, 18:15

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

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Answers (1)
1. 5 September, 20:03
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F (t) = 4t² - 8t + 7

f (t) = 4 (t² - 2t) + 7

f (t) - 7 = 4 (t² - 2t - __)

t² ⇒ t * t

2t ⇒ 2 * 1t

1² ⇒ 1 * 1

f (t) - 7 + 4 (1) = 4 (t² - 2t + 1)

(t-1) (t-1) = t (t-1) - 1 (t-1) = t² - t - t + 1 = t² - 2t + 1

f (t) = 4 (t-1) ² + 3
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