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 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

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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edwarddfairsroy6j7i edwarddfairsroy6j7i · Answer 2 · 2020-04-29T19:01:27+02:00

Answer:

A f(1) =4(1)^2 – 8(1) +7 min height 3

Step-by-step explanation:

The function is a parabola, and the problem asks to transform the equation into f(t)=a(x-h)2 + k

Given f(t) = 4t2 -8t +7

= (4t2 - 8t + 4) + 7 - 4

=4 (t2 - 2t + 1) + 3

= 4 (t-1) 2 +3

This removes C and D from the viable choices.

Differentiating the f(t),

f’(t) = 8t – 8, the maximum/minimum value occurs at f’(t) = 0

0 = 8t – 8

t = 1

determining if maximum or minimum, f”(t) > 0 if minimum, f”(t) < 0 maximum

f”(t) = 8 > 0, therefore minimum

f(1) =4(1)^2 – 8(1) +7

= 3

Therefore, minimum height is 3.