Problem preview

F-IF.7.a Warmup M1-025-A14-V04

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

Interpret a quadratic graph feature in context

Problem

Profit $P(x)$, in dollars, for $x$ whole smoothies sold is a downward-opening quadratic with zeros $x~=~10$ and $x~=~40$. Interpret the break-even points and determine where profit and loss occur within the model.

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profit = positive for x<10 and x>40 because parabola opens down

zeros = P(0)=10 and P(0)=40; break-even at $10 and $40

profit = positive only at x=10 and x=40; between them P(x)<0

zeros = P(10)=0 and P(40)=0; events = break-even at 10 and 40 smoothies; profit = P(x)>0 for 10<x<40; loss = P(x)<0 for 0≤x<10 and x>40 within the model; conclusion = whole-number sales strictly between 10 and 40 yield positive profit

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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

Profit \(P(x)\), in dollars, for \(x\) whole smoothies sold is a downward-opening quadratic with zeros \(x~=~10\) and \(x~=~40\). Interpret the break-even points and determine where profit and loss occur within the model.

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