Learn Before
Using to Model the Height of a Dropped Stone
A polynomial function can model the height of a falling object over time. For instance, the function describes the height in feet of a stone seconds after it is dropped from a cliff that is feet tall. To find the initial height of the object—the height at the exact moment it is dropped—evaluate the function at seconds. Substituting for gives . The squared term becomes , and multiplying by still yields . Adding results in . Thus, the initial height is feet, confirming it matches the height of the cliff.
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Intermediate Algebra @ OpenStax
Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
Algebra
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Using to Model the Height of a Dropped Stone
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Using to Model the Height of a Dropped Ball
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Remainder Theorem
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Imagine your company uses a polynomial function, , to model projected weekly profit based on , the number of products manufactured. Your manager asks you to evaluate this profit function for an input of 500 products. Which sequence of steps correctly describes the mathematical procedure you must follow?
A facility manager uses a mathematical expression to estimate the weight capacity of a storage floor based on its thickness. To find the capacity for a specific thickness, the manager must evaluate the expression. Arrange the steps of this evaluation process in the correct sequence.
Procedural Steps for Evaluating Models
An operations manager at a logistics company uses polynomial functions to predict fuel consumption based on vehicle weight. To analyze these models correctly, the manager must understand the specific components of the mathematical process. Match each term with the description of its role in this analysis.
A logistics company uses a polynomial function to model fuel consumption based on vehicle speed. True or False: To evaluate this function for a specific speed, that value must be substituted for the variable in every term of the polynomial expression before the order of operations is used to simplify the result.
Learn After
As a safety coordinator for a commercial construction site, you are analyzing an incident where a heavy steel bolt fell from a work platform. The height of the bolt in feet, seconds after it was dropped, is modeled by the polynomial function . To mathematically determine the exact initial height of the platform right before the bolt was dropped, which specific procedure must you recall and perform?
A safety coordinator at a distribution center uses the polynomial function to model the height of a handheld scanner seconds after it falls from a storage mezzanine. To determine the initial height of the mezzanine using this model, the coordinator must evaluate the function by substituting the value ____ for .
An industrial safety technician is investigating an incident where a wrench was dropped from a maintenance platform. The height of the wrench in feet is modeled by the polynomial function , where is the number of seconds since the drop. Match each component of this mathematical model to the real-world value or calculation role it represents.
A safety coordinator at an industrial site uses the polynomial function to model the height (in feet) of a tool seconds after it is dropped from a maintenance platform. Arrange the following steps in the correct order to recall the mathematical procedure for determining the initial height of the platform.
Safety Protocol: Initial Height Verification