Ozone occurs at all levels of Earth's atmosphere. The...

Name: Problem 38, Chapter 2: Precalculus: Functions and Graphs
Uploaded: 2021-05-24T22:03:12-08:00
Duration: 46 s
Channel: Lucas Finney

Ozone occurs at all levels of Earth's atmosphere. The density of ozone varies both seasonally and latitudinally. At Edmonton, Canada, the density $D(h)$ of ozone (in $10^{-3} \mathrm{cm} / \mathrm{km}$ ) for altitudes $h$ between 20 kilometers and 35 kilometers was determined experimentally. For each $D(h)$ and season, approximate the altitude at which the density of ozone is greatest. $$D(h)=-0.078 h^{2}+3.811 h-32.433 \text { (spring) }$$

Ozone occurs at all levels of Earth's atmosphere. The density of ozone varies both seasonally and latitudinally. At Edmonton, Canada, the density $D(h)$ of ozone (in $10^{-3} \mathrm{cm} / \mathrm{km}$ ) for altitudes $h$ between 20 kilometers and 35 kilometers was determined experimentally. For each $D(h)$ and season, approximate the altitude at which the density of ozone is greatest.
$$D(h)=-0.078 h^{2}+3.811 h-32.433 \text { (spring) }$$

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Key Concepts

Quadratic Functions

Quadratic functions are polynomial functions of the degree two, typically expressed in the form ax² + bx + c. They produce parabolic graphs that open upward if a is positive and downward if a is negative, indicating the potential for a minimum or maximum point in the function, respectively.

Vertex of a Parabola

The vertex of a parabola is the point at which the function attains its extreme value (either maximum or minimum). It can be computed using the formula h = -b/(2a) in the context of quadratic functions, which helps determine the precise location where the function reaches its peak or trough.

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