SOLUTION: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be      Log On


   

Question 1032910: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?
Thank you very much
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The x-value for the vertex ( maximum in this case )
is given by the formula:
+x%5Bmax%5D+=+-b%2F%282a%29+ when the equation has the form
+P%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+-22.5+
+b+=+428+
+x%5Bmax%5D+=+-428+%2F+%28+2%2A%28-22.5%29+%29+
+x%5Bmax%5D+=+9.5111+
The population is highest in June of 1999