In one U.S. city, the quadratic function models the median, or average, age, y, at which men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)
To find the year when the average age at first marriage was at a minimum, we need to analyze the quadratic function that models the data. Let's start by understanding the general form of a quadratic function:
y = ax^2 + bx + c
In this case, the independent variable x represents the number of years after 1900, and y represents the median age at which men were first married.
Since we are looking for the year when the average age is at a minimum, we need to find the vertex of the quadratic function. The x-coordinate of the vertex represents the year, and the y-coordinate represents the average age at first marriage.
The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:
x = -b / (2a)
Based on the given information, we can assume that the quadratic function provided is in standard form, y = ax^2 + bx + c. However, we need specific values for the coefficients a, b, and c in order to calculate the coordinates of the vertex.
Since these coefficients are not given, we need more information before we can determine the specific year and the average age at first marriage.
y= ax^2+bx+ c
using calculus...
dy/dx=2ax+b=0
x=-b/2a is either the max, or min.
You need more information...