To analyze the height of an object thrown upward, modeled by the polynomial function $h(t) = -16t^2 + 48t + 160$, we can find its zeros, the time it reaches a specific height, and its height at a specific time. First, to find the zeros which indicate when the object hits the ground, set $h(t) = 0$. Factoring the equation $-16t^2 + 48t + 160 = 0$ gives $-16(t^2 - 3t - 10) = 0$, which factors further to $-16(t - 5)(t + 2) = 0$. This yields $t = 5$ and $t = -2$. Discarding the negative time, the object hits the ground at 5 seconds. Second, to find when the object is at a specific height of 160 feet, set $h(t) = 160$. Subtracting 160 from both sides gives $-16t^2 + 48t = 0$. Factoring gives $-16t(t - 3) = 0$, yielding $t = 0$ and $t = 3$. The object is at 160 feet at 0 and 3 seconds. Third, to find the height at a specific time, such as $t = 1.5$ seconds, substitute 1.5 into the function. The result is $h(1.5) = -16(1.5)^2 + 48(1.5) + 160 = 196$. The object is at 196 feet after 1.5 seconds.