Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build an explicit model from context and solve for the input that gives a target output
Problem
A ball's height is \(h(t)=-16t^{2}+64t~\text{feet}\) from launch until it lands. Solve \(h(t)=0\) by factoring, list every candidate time, apply the launch-to-landing domain, and interpret each retained time in the motion.
Big Picture
What this problem is really about
Ground events occur when the height output is zero, and the variable greatest common factor must be kept because it represents one of those times. We’ll factor the equation, solve every zero-product branch, check the candidates against the launch-to-landing interval, and interpret the retained endpoints as distinct motion events.
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