# problem solving for a test tomorrow!!!

• Feb 24th 2010, 09:42 PM
Tessarina
problem solving for a test tomorrow!!!
A company first started recording their profit making in december 2007, before the financial crisis. They recorded it quarterly for 2 years. It is recorded in 1000's dollars.
P(t) = t^2-9t+14

(x intercepts: 2 and 7)
(y intercept: 14)
(vertex: 4.5, -6.25)
Questions:
1) When the company recorded its lowest profit, what quarter did this happen in?

2) when did there profit first start to rise?

3) Find P(t) when t=0

4) When did the profit reach 20 000 dollars?

5)calculate k if the company made no loss.
P(t) = t^2-9t+14+k
• Feb 24th 2010, 09:51 PM
drewbear
is t years?
• Feb 24th 2010, 10:25 PM
Tessarina
T isn't years, its for the quarterly times.

T is the x asis, and the y axis is for the profit.
• Feb 24th 2010, 10:57 PM
drewbear
oh ok, my apologies. i was unclear.

1) the lowest profit would occur at the vertex, so 4.5, which i assume would be part of the first quarter of the second year.

2) the profit first started to rise right after the vertex, after x=4.5, but it didnt actually become positive until the x-intercept x=7

3) $P(t)=t^2-9t+14$

$P(0)=(0)^2-9(0)+14$

$P(0)=14$

4) $20=t^2-9t+14$

$
0=t^2-9t-6
$

$
\frac{-b+/-\sqrt{b^2-4ac}}{2a}
$

$
\frac{9+\sqrt{(-9)^2-4(1)(-6)}}{2(1)}
$

$
\frac{9+\sqrt{81+24}}{2}
$

$
\frac{9+\sqrt{105}}{2}
$

$
x=9.623ish
$

so since this is only for the first two years, the profit has not reached \$20,000 yet.

5) im not sure what exactly part 5 means.sorry(Crying)
• Feb 24th 2010, 11:02 PM
Tessarina
Thank you so much !
Im sorry the information i gave was so sketchy, we had a test today and it was all i cold remember of the question i didnt understand.
:):)