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Properties of Parabolas

Source: Female Farmer - pixdeluxe/E+/Getty Images 

Optimization 

Sources: Pilot - Nikontiger/E+/Getty Images; Inspector - milanvirijevic/E+/Getty Images

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Lesson Goals

  • Recognize parabola terminology: vertex, zeros, axis of symmetry, and optimum (maximum or minimum) value.
  • Identify the vertex, zeros/\(x\)-intercepts, axis of symmetry, and optimum value of a parabola given its table of values or graph.
  • Interpret the meanings of a parabola's vertex, zeros/\(x\)-intercepts, axis of symmetry, and optimum value within a given context.

Try This

Marsha plans to build a rectangular fenced area for her chickens. She has \(20\) metres of fencing in total.

She will enclose an area beside her barn so she only needs to use fencing on three sides.

Determine the maximum area that she can enclose.