Question

The function f(t) = 4t2 − 8t + 8 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 + 2; the minimum height of the roller coaster is 2 meters from the groundf(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 4 meters from the groundf(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the groundf(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground

Answer 1

f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground

Explanation:

The function is a quadratic where t is time and f(t) is the height from the ground in meters. You can write the function f(t) = 4t2 − 8t + 8 in vertex form by completing the square. Complete the square by removing a GCF from 4t2 - 8t. Take the middle term and divide it in two. Add its square. Remember to subtract the square as well to maintain equality.

f(t) = 4t2 − 8t + 8

f(t) = 4(t2 - 2t) + 8 The middle term is -2t

f(t) = 4(t2 - 2t + 1) + 8 - 4 -2t/2 = -1; -1^2 = 1

f(t) = 4(t-1)^2 + 4 Add 1 and subtract 4 since 4*1 = 4.

The vertex (1,4) means at a minimum the roller coaster is 4 meters 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 4 meters from the ground
• f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the ground
• f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground