Regents Exam Questions CC.A.REI.11: Quadratic-Linear Systems
Page 1
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Name: __________________________________
CC.A.REI.11: Explain why the x-coordinates of the points where the graphs of the
equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x);
find the solutions approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.
1 If
value of x is
1)
and
2)
and 4
3)
and 0
4) 4 and 0
and
, for which
?
2 A pelican flying in the air over water drops a
crab from a height of 30 feet. The distance the
crab is from the water as it falls can be
represented by the function
,
where t is time, in seconds. To catch the crab
as it falls, a gull flies along a path represented
by the function
. Can the gull
catch the crab before the crab hits the water?
Justify your answer. [The use of the
accompanying grid is optional.]
3 John and Sarah are each saving money for a
car. The total amount of money John will save
is given by the function
. The
total amount of money Sarah will save is given
by the function
. After how many
weeks, x, will they have the same amount of
money saved? Explain how you arrived at
your answer.
4 The price of a stock,
, over a 12-month
period decreased and then increased according
to the equation
, where x
equals the number of months. The price of
another stock,
, increased according to the
equation
over the same 12month period. Graph and label both equations
on the accompanying grid. State all prices, to
the nearest dollar, when both stock values
were the same.
Regents Exam Questions CC.A.REI.11: Quadratic-Linear Systems
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1 ANS: 2
REF: 081517ai
2 ANS:
Yes.
.
.
REF: 060228b
3 ANS:
John and Sarah will have the same amount of money saved at 7 weeks. I set the
expressions representing their savings equal to each other and solved for the positive value of x by
factoring.
REF: 061527ai
4 ANS:
Regents Exam Questions CC.A.REI.11: Quadratic-Linear Systems
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$9, $6.
REF: 060328b
.