The graph shows a quadratic function of the form P ( t ) = a t 2 + b t + c which represents the yearly profit for a company, where P ( t ) is the profit in year t . (a) Is the value of a positive, negative, or zero? Explain. (b) Write an expression in terms of a and b that represents the year t when the company made the least profit. (c) The company made the same yearly profits in 2008 and 2016. Estimate the year in which the company made the least profit.
The graph shows a quadratic function of the form P ( t ) = a t 2 + b t + c which represents the yearly profit for a company, where P ( t ) is the profit in year t . (a) Is the value of a positive, negative, or zero? Explain. (b) Write an expression in terms of a and b that represents the year t when the company made the least profit. (c) The company made the same yearly profits in 2008 and 2016. Estimate the year in which the company made the least profit.
Solution Summary: The author explains that the value of a is positive, since the graph of the function is symmetrical about its vertex. The year in which the company made the least profit is 2012.
The graph shows a quadratic function of the form
P
(
t
)
=
a
t
2
+
b
t
+
c
which represents the yearly profit for a company, where
P
(
t
)
is the profit in year
t
.
(a) Is the value of
a
positive, negative, or zero? Explain.
(b) Write an expression in terms of
a
and
b
that represents the year
t
when the company made the least profit.
(c) The company made the same yearly profits in 2008 and 2016. Estimate the year in which the company made the least profit.
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