Problem preview

F-BF.1.a Warmup M2-014-A13-V03

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Write an explicit function model from a verbal situation and evaluate it

Problem

The height of an object is \(h(t)=-16t^{2}+48t+5~\text{feet}\) after \(t~\text{seconds}\). Evaluate \(h(2)\), showing the parenthesized substitution and arithmetic in the correct order, then state the height with units.

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h(2) = −16(2)² + 48(2) + 5 = −64 + 96 + 5. The squared input must be evaluated within the coefficient multiplication; the displayed expression is not a valid substitution explanation.

The height is 37 feet. No substitution or arithmetic shows how the value was obtained.

h(2) = −16(2²) + 48(2) + 5 = −64 + 96 + 5 = 37, so the height is 37 feet.

h(2) = 37 seconds. The output h is height, so its unit is feet, not seconds.

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Curriculum context

Course: Math II
Standard: F-BF.1.a
Category: Functions
Domain: Building Functions
Objective: Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type: Write an explicit function model from a verbal situation and evaluate it