Final answer:
The correct roller coaster height equation from the given options is h = -0.046t² + 5t + 75. This quadratic equation is emblematic of the motion of an object projected upwards with an initial velocity and then descending under the force of gravity.
Step-by-step explanation:
The equation h = -0.046t² + 5t + 75 represents the height (h) of a roller coaster at any given time (t) in seconds. To understand this equation, let's consider the quadratic formula. The quadratic formula provides the roots (solutions) of the equation at² + bt + c = 0, which are -b ± √(b² - 4ac) / 2a.
With the given equation, the coefficient a is -0.046, b is 5, and c is 75. The application of the quadratic formula would yield the times at which the roller coaster reaches the ground level if h=0. Only positive values of time are feasible as negative time values would imply a backward calculation in time before the starting point, which is not physically meaningful in this context.
The correct form of the roller coaster height equation from the options provided is the one given at the start, which correlates with the concept of initial velocity and the effects of gravity on the object in motion. This type of motion reflects an initial upward velocity and a subsequent descent affected by gravity.