Mathematics: 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). (a) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground (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

The function f(t) = 4t2 − 8t + 7 shows the height

sarah19Nursing

31.12.2021

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.

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destiny465

04.04.2021

x=27.5

y=49.75

Step-by-step explanation:

$4x=180-70-40\\4x=70\\x=27.5$

$2y-17=180-70-27.5\\2y-17=82.5\\2y=99.5\\y=49.75$

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