The function f(t) = 4t2 − 8t + 6 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

The correct option is 3.

Step-by-step explanation:

The vertex form of a parabola is

           .... (1)

where a, h, and k are integers, and interpret the vertex of f(t). (h,k) is the vertex of the parabola.

The given function is

It can be written as

If an expression is defined as , then we need to add to make it perfect square.

In the expression the value of b is -2. So, we nned to add and subtract in the parenthesis.

               .... (2)

The vertex form of the parabola is .

From (1) and (2), we get h=1 and k=2. It means the vertex of the parabola is (1,2). Vertex of upward parabola is point of minima. So the  minimum height of the roller coaster is 2 meters from the ground.

Therefore the correct option is 3.

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