Question

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).
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

Answer 1

F(t) = $4 t^{2} -8+6$
The formula to use is: a(x-xv)^2+yv
where a is the coeficient of x^2, xv= -b/2a (b is the coeficient of x) and yv= -delta/4a or f(xv)

xv = 8/8 =1
yv = f(xv)=f(1) = 2

f(t) = 4(t-1)^2+2 the minimum value is 2 when t=1

The answer to your question is C. I hope this is the answer that you are looking for and it comes to your help.