Question

The quadratic function y = -0.642m? + 8.547x + 73.977 models the highest recorded temperatures in 2012 in Jacksonville, where a = 1 represents January and y represents the temperature, in degrees Fahrenheit (° F). Use the model to determine which month(s) had a high temperature of about 101°F

Answer 1

To find the month(s) that had a high temperature of about 101°F, we need to solve the equation:

`-0.642m^2 + 8.547x + 73.977 = 101`

We can use the quadratic formula to find the values of m that satisfy this equation:

`m = (-b \pm √(b^2 - 4ac))/(2a)`

where a = -0.642, b = 8.547, and c = 73.977 - 101 = -27.023.

Plugging in these values, we get:

`m = (-8.547 \pm √(8.547^2 - 4(-0.642)(-27.023)))/(2(-0.642))`

`m \approx 6.76 \text{ or } 6.24`

Since m represents the month, we need to round these values to the nearest integer. Therefore, the months that had a high temperature of about 101°F are:

- July (m = 7)

- June (m = 6)