Final answer:
The function h(t) = -4t^2 + 32t is a quadratic equation that models the path of a projectile. It gives the height in feet as a function of time in seconds, describing vertical motion under gravity with an initial upward velocity.
Step-by-step explanation:
The quadratic function h(t) = -4t^2 + 32t models the vertical motion of a projectile. This function represents the height h in feet as a function of time t in seconds. The coefficients of this quadratic equation are -4 for a (acceleration due to gravity, as represented by the coefficient of the t2 term), 32 for b (initial upward velocity), and there's no c term since the object is launched from ground level (height 0).
To find the times when the object is at a certain height, one would typically set h(t) equal to that desired height and use the quadratic formula to solve for t. In scenarios involving quadratic motion equations, we ignore the negative time value because it has no physical meaning in the context of a forward-moving timeline.