Answer:
Quadratic
Explanation:
The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches it maximum height and then starts dropping back to ground at increasing speeds due to positive acceleration exerted by the force of gravity.
The flight path of the parabola can thus be modeled by height as a function of elapsed time
h = f(t) where f(t) is a quadratic equation in t with the general form being
a · t² +b · t + c
We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever
The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However we know from observation that the firework has the highest speed at the moment of launch
Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.
The note says:
Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.
Indeed the actual path of the firework is a reflection of the graph about the x axis. so that it is a downward facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.
The height would be the y axis and time t the x-axis