Question

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 highest amount of precipitation?


Month (x)

Precipitation

January

2.27 inches

February

?

March

?

April

?

May

?

June

?

July

?

August

?

September

2.59 inches

October

?

November

?

December

?



Sketch a graph or fill in the table to answer the question.
April
May
June
July

Answer 1

Using the vertex of a quadratic function, it is found that Phoenix received the highest amount of precipitation on the month of May.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

$x_v = -\frac{b}{2a}$

$y_v = -\frac{b^2 - 4ac}{4a}$

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 precipitation each month x in Phoenix is given by:

$y = -0.04088x^2 + 0.4485x + 1.862$

Hence the coefficients are a = -0.04088, b = 0.4485, c = 1.862, and the month for which the precipitation will be highest is given by:

$x_v = -\frac{0.4485}{2(-0.04088)} = 5.48$

Hence during the month of May.

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