The total-cost model is $T(x)=x^{2}+8x+12$ dollars for $x\ge~0$. Find its $y\text{-}\text{intercept}$ by evaluating $T(0)$, state the intercept as an ordered pair, and interpret the output as an initial or fixed cost.

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The y-intercept is (12, 0) because 12 is the constant term. A y-intercept has input 0, so its coordinates are not reversed.

At x = 0, T(0) = 12, so the y-intercept is (0, 12): the modeled initial total cost is $12.

Set T(x) = 0 to find the y-intercept. That procedure finds zeros, while a y-intercept is found by setting x = 0.

At x = 0, T(0) = 0, so the y-intercept is (0, 0). Substituting 0 leaves the constant term 12.

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Curriculum context

Course: Math II
Standard: F-BF.1.b
Category: Functions
Domain: Building Functions
Objective: Combine standard function types arithmetically to create models.
Problem type: Interpret a named feature of a combined function model in context