Determine the quadratic function whose graph is given.
-The quadratic function f(x) = 0.0041x² - 0.48x + 36.42 models the median, or average, age, y, at which U.S. 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.)

Question

Quizplus · Accepted Answer

The minimum value of a quadratic function $f(x) = ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$. For the given function $f(x) = 0.0041x^2 - 0.48x + 36.42$, $a = 0.0041$ and $b = -0.48$. Thus, the year of minimum age is $x = -\frac{-0.48}{2(0.0041)} = 58.54$, which rounds to 1959 when added to 1900. Substituting $x = 58.54$ into the function gives the minimum average age, which rounds to 22.4 years.

Determine the Quadratic Function Whose Graph Is Given