Can someone help with this profit and renevue ditto- it's 10th grade math (my brothers)??

Question

1) profit for company: P(x) = -2.9x^2 + 28.4x - 40.2
x is number of years and P(x) is profit in thousands of dollars.

(a) Find year the company saw profit.
(b) Find the year the company hahd the highest profit and what profit was.
(c) Find the year the company begins to lose money,


- I totally forgot how to do this stuff but remember a little. If someone could remind me what to do to start it off, I can help him out. THANKS!! :)

Answer 1

a)
-2.9 x^2+28.4x -40.2 =0
2.9x^2-28.4 x+40.2=0
29x^2 -284 x +402 =0

x= [142 +/- 92.22]/29
so
x=[142 +92.22]/29 = 234.22 /29 =8.076
or
x=(142-92.22)/29 =191.78 /29=6.61

so the company will start to gain profit in the 7th year ( the answer 6.61)
and start to lose money ar 9th year (8.076 )
for the highest profit get p' (x)=0
& it is (by logic ) the eight year

Answer 2

Clues:
The year they first saw profit and the year they began to lose money are both when P=0, first when it crosses the Y=0 line heading up, and the second whan it crosses it going down.

The highest profit can be found by solving the derivative for P = 0, at the peak, the slope of the curve is 0.

P' = -2.9x +28.4

Answer 3

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