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 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

A. ; the minimum height of the roller coaster is 3 meters from the ground.

Step-by-step explanation:

The given function is,

As the leading coefficient is 4 which is positive, so the parabola will open upward and at the vertex the value of the function will be minimum.

So the vertex form will be,

Hence the vertex will be at

At vertex the value of the function ot f(t) is 3, so the minimum height of the roller coaster is 3 meters from the ground.

Option A- ; the minimum height of the roller coaster is 3 meters from the ground.

Step-by-step explanation:

Given : The function shows the height from the ground f(t), in meters, of a roller coaster car at different times t.

To find : Write f(t) in the vertex form , where a, h, and k are integers, and interpret the vertex of f(t).

Solution :

We have given the function

As the leading coefficient is 4 which is positive, so the parabola will open upward and at the vertex the value of the function will be minimum.

Now, we convert it into vertex form,

Making completing square,

So the vertex form will be,

Where Vertex are (h,k)=(1,3) and a=4

At vertex the value of the function f(t) is 3.

So, the minimum height of the roller coaster is 3 meters from the ground.

Therefore, Option A is correct.