Question

The path of a firework can be modeled with the function: f(t) = −8t^2+64t+3f where t is the time in seconds after the firework launched.

Which of the following statements are TRUE?
a) The maximum height of the firework is 3 feet.
b) The maximum height of the firework is 131 feet.
c) The maximum height of the firework is 227 feet.
d) The firework reaches its maximum height 4 seconds after it is launched.
e) The firework reached its maximum height 8 seconds after it is launched.

Answer 1

B, D

Explanation:

This can be determined by finding the vertex of the parabola represented by the function f(t) = −8t^2+64t+3f.

The x-coordinate of the vertex is -b/2a,

which in this case is -64/(-8) = 4 seconds.

The y-coordinate of the vertex is

f(4) = -8(4)^2 + 64(4) + 3 = -8(16) + 256 + 3 = -128 + 259 = 131 feet, which is the maximum height of the firework.