Answer:
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.