Problem

\(h(t)=-16(t-2)^{2}+80\) models ball height \(h~\text{in}~\text{feet}\) for \(t\ge~0~\text{seconds}\) until landing. Verify the vertex lies in the contextual domain, then identify vertex, opening, extremum type, contextual input/unit, contextual output/unit, and model interpretation.

Big Picture

What this problem is really about

Vertex form gives the candidate turning point directly, but the context determines whether that point occurs during the modeled flight. We’ll read time and height from the vertex, compare the vertex time with the nonnegative launch-to-landing domain, and use the negative leading coefficient to decide the opening direction and extremum type.

Answer choices

Choose your path.

Preview only

vertex=(2,80); opening=down; extremum type=minimum; contextual input=2 seconds; contextual output=80 feet; interpretation=modeled ball reaches minimum height80 feet at2 seconds

vertex=(-2,80); opening=down; extremum type=maximum; contextual input=-2 seconds; contextual output=80 feet; interpretation=modeled ball reaches maximum height80 feet at-2 seconds

vertex=(80,2); opening=down; extremum type=maximum; contextual input=80 seconds; contextual output=2 feet; interpretation=modeled ball reaches maximum height2 feet at80 seconds

vertex=(2,80); opening=down; extremum type=maximum; contextual input=2 seconds; contextual output=80 feet; interpretation=modeled ball reaches maximum height80 feet at2 seconds

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

\(h(t)=-16(t-2)^{2}+80\) models ball height \(h~\text{in}~\text{feet}\) for \(t\ge~0~\text{seconds}\) until landing. Verify the vertex lies in the contextual domain, then identify vertex, opening, extremum type, contextual input/unit, contextual output/unit, and model interpretation.

What this problem is really about

Turn the preview into practice.

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