Question

The average annual income, l, in dollars, of a lawyer with an age of x years is modeled with the following function:

I = -425x^2 + 45,000x - 650,000

According to this model, what is the maximum average annual income, in dollars, a lawyer can earn? Round to the nearest whole dollar.

okay, i can't figure this out. every time i plug it in to the quadratic formula i get a low number like 90 or 16. i'm terrible with word problems, can someone try to walk me through this?

Answer 1

i tried it twice more and this time got 69 and then 354 so obviously i don't know what i'm doing :(

Answer 2

Hey, I'm sorry but I'm going right now (for a while), maybe if you're online later, I can help you. But maybe someone will help you by the time I come back online, take care and good luck.

I will get back to you later.

Answer 3

@iambatman okay, sounds good. thanks anyways!

Answer 4

The question is asking for annual income, and thus that means that x=1.
In your question, the equation for income is \(\normalsize\color{red}{ \rm I = -425x^2 + 45,000x - 650,000 }\)
And x is the number of years. So for annual income, x=1. Plug that in and find y.

\(\normalsize\color{blue}{ \rm I = -425x^2 + 45,000x - 650,000 }\)
\(\normalsize\color{blue}{ \rm I = -425~\color{orangered}{(1)}^2 + 45,000~\color{orangered}{(1)} - 650,000 }\)
\(\normalsize\color{blue}{ \rm I = -425 + 45,000 - 650,000 }\)
\(\normalsize\color{blue}{ \rm I = -605425 }\)

Answer 5

Something that really seems to be the correct solution comes out to make no sense what so ever -:(

Answer 6

@SolomonZelman thank you so much anyway, according to the work my teacher sent me i was supposed to graph the function and find it's vertex, but that wasn't how i was taught so i'm still a little confused

Answer 7

-425x^2 + 45,000x - 650,000 is in the form ax^2 + bx + c

where

a = -425
b = 45000
c = -650000

Answer 8

the x coordinate of the vertex is found using this formula

x = -b/(2a)

so plug in a = -425 and b = 45000 to get

x = -b/(2a)

x = -(45000)/(2(-425))

x = 52.941176 <--- this is approximate

Once you have the x coordinate of the vertex, you plug this x value back into y = -425x^2 + 45,000x - 650,000 to get the y coordinate of the vertex. I'll let you do this part.

Answer 9

@jim_thompson5910 I got the y-coordinate as 541,176.47 is that wrong?

Answer 10

I'm getting the same as well