Problem preview

F-LE.6 Warmup M2-027-A10-V02

Apply quadratic functions to physical situations such as projectile motion under gravity.

Build a complete projectile sketch record

Problem

Build the complete physical-flight sketch record for \(h(t)=-16t^{2}+32t+48\). Factor to find \(\text{both}~\text{algebraic}~\text{roots}\), identify the negative root as nonphysical, evaluate launch height at \(t=0\), calculate the vertex, and state opening, landing, physical domain, and range.

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Launch (−1,0); vertex (1,64); landing (3,0); domain [−1,3]; range [0,64].

Launch (0,48); vertex (2,48); landing (3,0); domain [0,3]; range [0,48].

Launch (0,48); vertex (1,64); landing (3,0); opens down; domain [0,3]; range [0,64]; root −1 is nonphysical.

Launch (0,−48); vertex (1,−64); landing (3,0); opens up; domain [0,3].

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Curriculum context

Course: Math II
Standard: F-LE.6
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Apply quadratic functions to physical situations such as projectile motion under gravity.
Problem type: Build a complete projectile sketch record