Apply quadratic functions to physical situations such as projectile motion under gravity.
Interpret equal-height projectile times by symmetry
Problem
Interpret the equal-height times \(t=1\) and \(t=3\) for \(h(t)=-16(t-2)^{2}+64\). Evaluate the common height, average the times to recover the symmetry axis and peak time, compare each time with the peak, and label the ascending and descending phases with units.
Big Picture
What this problem is really about
Equal outputs on a projectile parabola come from inputs equally spaced around its symmetry axis. We’ll verify the shared height, average the two times to recover the peak time, and use each time’s position relative to the peak to label the rising and falling phases.
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