To determine which month Phoenix received the highest amount of precipitation, we will first calculate the monthly precipitation values using the given function: [tex]\( y = -0.04088x^2 + 0.4485x + 1.862 \)[/tex], where [tex]\( x \)[/tex] represents the month (1 for January, 2 for February, and so on until 12 for December).
Let's calculate the precipitation for each month from January to December:
1. January ([tex]\( x = 1 \)[/tex]):
[tex]\[
y = -0.04088(1)^2 + 0.4485(1) + 1.862 = 2.27 \text{ inches}
\][/tex]
2. February ([tex]\( x = 2 \)[/tex]):
[tex]\[
y = -0.04088(2)^2 + 0.4485(2) + 1.862 = 2.60 \text{ inches}
\][/tex]
3. March ([tex]\( x = 3 \)[/tex]):
[tex]\[
y = -0.04088(3)^2 + 0.4485(3) + 1.862 = 2.84 \text{ inches}
\][/tex]
4. April ([tex]\( x = 4 \)[/tex]):
[tex]\[
y = -0.04088(4)^2 + 0.4485(4) + 1.862 = 3.00 \text{ inches}
\][/tex]
5. May ([tex]\( x = 5 \)[/tex]):
[tex]\[
y = -0.04088(5)^2 + 0.4485(5) + 1.862 = 3.08 \text{ inches}
\][/tex]
6. June ([tex]\( x = 6 \)[/tex]):
[tex]\[
y = -0.04088(6)^2 + 0.4485(6) + 1.862 = 3.08 \text{ inches}
\][/tex]
7. July ([tex]\( x = 7 \)[/tex]):
[tex]\[
y = -0.04088(7)^2 + 0.4485(7) + 1.862 = 3.00 \text{ inches}
\][/tex]
8. August ([tex]\( x = 8 \)[/tex]):
[tex]\[
y = -0.04088(8)^2 + 0.4485(8) + 1.862 = 2.83 \text{ inches}
\][/tex]
9. September ([tex]\( x = 9 \)[/tex]):
[tex]\[
y = -0.04088(9)^2 + 0.4485(9) + 1.862 = 2.59 \text{ inches}
\][/tex]
10. October ([tex]\( x = 10 \)[/tex]):
[tex]\[
y = -0.04088(10)^2 + 0.4485(10) + 1.862 = 2.26 \text{ inches}
\][/tex]
11. November ([tex]\( x = 11 \)[/tex]):
[tex]\[
y = -0.04088(11)^2 + 0.4485(11) + 1.862 = 1.85 \text{ inches}
\][/tex]
12. December ([tex]\( x = 12 \)[/tex]):
[tex]\[
y = -0.04088(12)^2 + 0.4485(12) + 1.862 = 1.36 \text{ inches}
\][/tex]
To find the month with the highest precipitation:
- May ([tex]\( x = 5 \)[/tex]) has the highest precipitation value of [tex]\( 3.08 \)[/tex] inches.
Thus, the month in which Phoenix received the highest amount of precipitation is May.
