Maximum and Minimum Models

Learn and apply maximum and minimum models using equations, examples, and interpretation.

Lesson 4 of 53 parts Practice Flashcards

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Quadratic Optimization

Objective: Explain and use quadratic optimization in an Algebra 1 problem.

A parabolic model may predict an extreme value at its vertex; context and domain decide whether that point is feasible. Yes, so it may not be the feasible optimum.

Worked examples

Try itExample 1.1: For y=(x−5)²+17, what is the minimum y-value?Show answer

17. A nonnegative square has minimum zero; add the vertical shift. The answer is 17.

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Quadratic Optimization

Objective: Explain and use quadratic optimization in an Algebra 1 problem.

A parabolic model may predict an extreme value at its vertex; context and domain decide whether that point is feasible. Yes, so it may not be the feasible optimum.

Worked examples

Try itExample 1.1: For y=(x−5)²+17, what is the minimum y-value?Show answer

17. A nonnegative square has minimum zero; add the vertical shift. The answer is 17.

Units and Meaning

Objective: Explain and use units and meaning in an Algebra 1 problem.

The vertex x-coordinate has input units and the vertex y-coordinate has output units; state both in a contextual answer. A vertex is an ordered pair with two meanings.

Worked examples

Try itExample 2.1: For y=(x−8)²+27, what is the vertex x-coordinate?Show answer

8. Vertex form reveals the horizontal coordinate where the square is zero. The answer is 8.

Model Limitations

Objective: Explain and use model limitations in an Algebra 1 problem.

A quadratic fit may work over a limited range and should not be extended into physically impossible negative times or values without justification. Negative elapsed time is outside the described event.

Worked examples

Try itExample 3.1: For y=(x−11)²+37, what is the minimum y-value?Show answer

37. A nonnegative square has minimum zero; add the vertical shift. The answer is 37.

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