Problem preview

F-IF.7.a Warmup M1-025-A14-V02

Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.

Interpret a quadratic graph feature in context

Problem

Projectile height \(H(t)\), in feet, is modeled on \(0~\le~t~\le~6\) seconds with \(x\text{-}\text{intercepts}\) \((0,~0)\) and \((6,~0)\), and the parabola is above the axis between them. Interpret the zeros as events, the sign between them, and the contextual domain.

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domain = (-∞,∞) because every quadratic has all-real algebraic domain

zeros = H(0)=6 and H(0)=0; events = starts 6 feet high

between = H(t)<0, so projectile is underground during flight

zeros = H(0)=0 and H(6)=0; events = projectile is at ground level at launch and again 6 seconds later; between = H(t)>0 for 0<t<6, so projectile is above ground; domain = [0,6] seconds

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Curriculum context

Course: Math I
Standard: F-IF.7.a
Category: Functions
Domain: Interpreting Functions
Objective: Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Problem type: Interpret a quadratic graph feature in context