The average income i in dollars of a lawyer with an age of x years is modeled with the following function: i=-425x^2+45,500x-650000 what is the youngest age for which the average income of a lawyer is $250000

The youngest age was 26.1843 years

Explanation:
The equation that models the average income is:
i = -425x² + 45500x - 650000
where:
i is the average income
x is the age

We are looking for the age at which the income was $250000.
Therefore, we will substitute with i = 250000 in the above equation and solve for x as follows:
250000 = -425x² + 45500x - 650000
425x² - 45500x + 650000 + 250000 = 0
425x² - 45500x + 900000 = 0

The general form of the quadratic equation is:
ax² + bx + c = 0

By comparison:
a = 425
b = -45500
c = 900000

Substitute in the quadratic formula shown in the attached image to get the values of x.

We will find that:
either x = 80.8744
or x = 26.1843

Since we are looking for the younger age, therefore, our answer would be:
26.1843 years

Hope this helps :)