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This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is
modeled by y = -0.04088x2 + 0,4485x + 1,862.
In what month did Phoenix receive the lowest amount of precipitation?

Month (x) Precipitation
January 2.27 inches
February?
March?
April?
May?
June?
July?
August?
September 2.59 inches
October?
November?
December

Respuesta :

Considering the vertex of the quadratic function, it is found that the month in which Phoenix received the highest amount of precipitation was May.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

  • [tex]x_v = -\frac{b}{2a}[/tex]
  • [tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

  • If a < 0, the vertex is a maximum point.
  • If a > 0, the vertex is a minimum point.

In this problem, the function is given by:

y = -0.04088x² + 0.4485x + 1862.

The coefficients are a = -0.04088 < 0, b = 0.4485, hence the month of the highest amount of precipitation was:

[tex]x_v = -\frac{0.4485}{2(-0.04088)} = 5.4[/tex]

Hence during the month of May.

More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967

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