Help me with this problem!!

Question

The equation P = –0.5t^2 – 3t + 8 describes the monthly profit (in millions of dollars) of ABCD Corp. for the year 2012, with t = 0 representing July 2012.

A.) How much profit did the corporation make in March 2012?

B.) How much profit did the corporation make in October 2012?

C.) Find the t-intercepts. What do they represent?

D.) Find the p-intercepts. What do they represent?

E.) Sketch the graph c )

Find the t-intercepts. What do they represent?

d)

Find the

P

-intercepts. What do they represent

c)

Find the t-intercepts. What do they represent?

d)

Find the

P

-intercepts. What do they represent

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3

c)

Find the t-intercepts. What do they represent?

d)

Find the

P

-intercepts. What do they represent

t + 8 describes the monthly profit (in millions of dollars) of ABCD

Corp. for the year 2012, with t = 0 representing July 201

Answer 1

P = -0.5t^2 - 3t + 8

A) P(-4) = -.5(16) +12 + 8 = 12 million profit March 2012

B) P(3) = -.5(9) -9 + 8 = -5.5 million loss for October 2012

C) 0=-.5t^2 -3t + 8

t^2 +6t -16 =0

(t+8)(t-2) = 0

t = 2 and -8

they represent the time when the profits =0, the break even times. t= 2 means the company breaks even September 2012 and t=-8 means the company breaks even November 2011

D) p intercept is 8. It means a profit of 8 million in July 2012.

There is only one p intercept

E) the graph is a parabola,

-.5t^2 -3t + 8

= -.5(t^2 +6t ) + 8

= -.5(t^2 +6t +9) + 8 + 9/2

= -.5(t+3)^2 + 25/2

It's a downward opening parabola with vertex = (-3, 12.5)= maximum point, axis of symmetry t=-3

plot t on the horizontal or x axis, p on the y or vertical axis

maximum profit is when t=-3

-.5(-3)^2 -3(-3) + 8 = -9/2 +9+8 = 12.5 million

the mid point in time between the break even times

April 2012 is half way between November 2011 and September 2012