Question

The daily high temperature in Death Valley, CA, in 2003 can be modeled by T(d) = -0.0018d^2 + 0.657d + 50.95, where T is the temperature in degrees Fahrenheit and d is the day of the year. What was the maximum temperature in 2003, to the nearest whole degree?

Answer 1

To find the maximum temperature in Death Valley, CA in 2003, we need to find the vertex of the parabolic equation model.

Step-by-step explanation:

To find the maximum temperature in 2003, we need to find the vertex of the parabolic equation represented by T(d) = -0.0018d^2 + 0.657d + 50.95. The vertex of a parabola in the form y = ax^2 + bx + c can be found using the formula x = -b/2a.

In this case, a = -0.0018 and b = 0.657. Plugging these values into the formula, we get x = -0.657 / (2 * -0.0018) = 182.638.

Since d represents the day of the year, the maximum temperature occurred on day 183. Plugging this value into the equation T(d), we get T(183) = -0.0018(183)^2 + 0.657(183) + 50.95 = 118.94.

Therefore, the maximum temperature in 2003 was 119 degrees Fahrenheit to the nearest whole degree.