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Groupon negotiates coupons for items discounted 50-90% off by having thousands of subscribers. As a result, it has experienced a big increase in value from October 2010 to March 2011. The function G(x) = 0.4x2 + 1.8x + 6, approximates the company\'s value, in billions of dollars, x months after October 2010. 1) What is the DOMAIN of this function? That is, what values are allowed for the variable \"x. (Hint: do negative values make sense?, is there a maximum value for a) x ?) b) The graph of the function will be a parabola (or a portion of one, depending on your answer to part (a)). Will that parabola open up or down? Attach a graph of G(x) c) Based on your answer to part (b), the function \"Value of Groupon\", G(x), will reacha maximum or a minimum? d) What is that maximum or minimum value? When will it be reached? e) Evaluate G(0) and interpret the meaning of that result. f Determine when Groupon\'s value was/ will be about $15 billion. ) The width of a computer screen is 3 inches more than its height. If the area of the screen is 154 square inches, a) Write an EQUATION that represents the problem. b) Solve the equation to determine the width of the screen. 6

Solution

G(x) = 0.4x^2 + 1.8x + 6

domain of the function is [ 0 , 5 ]

october 2010 - march 2011 = 5 months

negative values does not make sense as time cannot be negative

b) the graph of function is parabola opening upwards as leading coefficient is positive

c) value of groupon will not reach minimum as parabola is opening upwards but has minima for negative x value which is not possible

d) it will not reach the minimum

e) g(0) = 0.4(0)^2 + 1.8(0) + 6

= 6

this means in october 2010 company value was 6 billion dollars

f) 15 = 0.4x^2 + 1.8x + 6

0.4x^2 + 1.8 x -9 = 0

x = 3

so, after 3 months groupon value will be about 15 billion dollars