Answer:
The correct option is 3.
Step-by-step explanation:
The vertex form of a parabola is
\(f(x)=a(x-h)^2+k\) .... (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
\(f(x)=4t^2-8t+6\)
It can be written as
\(f(x)=4(t^2-2t)+6\)
If an expression is defined as \(x^2+bx\), then we need to add \((\frac{b}{2})^2\) to make it perfect square.
In the expression \(t^2-2t\) the value of b is -2. So, we nned to add and subtract \((\frac{-2}{2})^2\) in the parenthesis.
\(f(x)=4(t^2-2t+1^2-1^2)+6\)
\(f(x)=4(t^2-2t+1)+4(-1)+6\)
\(f(x)=4(t-1)^2-4+6\)
\(f(x)=4(t-1)^2+2\) .... (2)
The vertex form of the parabola is \(f(x)=4(t-1)^2+2\).
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.
