Final answer:
The path of a firework that did not explode is best modeled by a quadratic graph, representing its parabolic trajectory due to gravity.
Step-by-step explanation:
The question concerns which type of graph best models the path of a firework that did not explode. Given the options of linear, quadratic, and exponential graphs, the most accurate model for an unexploded firework's path would be a quadratic graph. When launching fireworks, they typically follow a projectile motion, which is best described by a parabolic path represented by a quadratic function. This path accounts for the initial upward motion and the subsequent downward motion due to gravity's influence on the firework, creating a curved trajectory. Linear and exponential graphs would not accurately depict this trajectory since linear graphs suggest a constant rate of increase or decrease, while exponential graphs imply growth that continuously increases at a faster rate, which does not reflect the action of gravity on a projectile.