Problem

For the ball-height model \(h(t)=-16t(t-3)\) on \(0\le~t\le~3~\text{seconds}\), solve each factor equation. Check both zeros against the domain and explain what zero height means at each admissible time.

Big Picture

What this problem is really about

Zeros of the height model are candidate times when the ball is at ground level. We’ll solve the time factors, ignore the nonzero scale as a source of roots, check every candidate against the closed time domain, and interpret the admissible endpoints as distinct ground events.

Answer choices

Choose your path.

Preview only

The zeros are t = 0 and t = 3, but they mean the time is 0 seconds at both values and the height is 3 feet at t = 3.

The zeros are t = 0 and t = −3. Only t = 0 is in the domain, so the ball is on the ground only at launch.

The zeros are t = 0 and t = 3, and they mean the ball reaches its maximum height at launch and at 3 seconds.

The zeros are t = 0 and t = 3, and both are in the domain. Height is 0 at ground level, so the ball is on the ground at launch and again 3 seconds after launch.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

For the ball-height model \(h(t)=-16t(t-3)\) on \(0\le~t\le~3~\text{seconds}\), solve each factor equation. Check both zeros against the domain and explain what zero height means at each admissible time.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.