To find the peak level of happiness, we need to determine the x-coordinate of the vertex of the parabolic equation y = -0.1012x^2 + 6.744x - 18.254.
The x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b / 2a.
In this case, a = -0.1012 and b = 6.744.
So, x = -6.744 / 2*(-0.1012) = -6.744 / -0.2024 = 33.333 hours.
Therefore, people report peak levels of happiness after approximately 33.333 hours of work.
To find the peak level of happiness, we substitute the x-coordinate of the vertex into the equation:
y = -0.1012(33.333)^2 + 6.744(33.333) - 18.254
y = -0.1012(1111.09) + 224.286 - 18.254
y = -112.535 + 224.286 - 18.254
y = 93.497
Therefore, the peak level of happiness reported by people is approximately 93.497.
Given the equation y = -0.1012x^2 + 6.744x - 18.254:
At how many hours worked do people report peak levels of happiness?
What is the peak level of happiness?
1 answer