Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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Name: __________________________________
CC.A.REI.4: Solve quadratic equations in one variable. a. Use the method of
completing the square to transform any quadratic equation in x into an equation of
the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from
this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking
square roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the quadratic
formula gives complex solutions and write them as a ± bi for real numbers a and b
1 Which value of k will make
a perfect square trinomial?
1)
2)
3)
4)
2 Brian correctly used a method of completing the square to solve the equation
. Brian’s first step was to rewrite the equation as
. He then
added a number to both sides of the equation. Which number did he add?
1)
2)
3)
4) 49
3 If
1)
2)
3)
4)
is solved by completing the square, an intermediate step would be
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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Name: __________________________________
4 Which step can be used when solving
1)
2)
3)
4)
5 If
1)
2)
3)
4)
by completing the square?
is solved by completing the square, one of the steps in the process is
6 When solving the equation
step in the process?
1)
2)
3)
4)
by completing the square, which equation is a
7 When directed to solve a quadratic equation by completing the square, Sam arrived at the
equation
. Which equation could have been the original equation given to
Sam?
1)
2)
3)
4)
8 Which equation has the same solution as
1)
2)
3)
4)
?
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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Name: __________________________________
9 Which equation has the same solutions as
1)
2)
3)
4)
?
10 Which equation is equivalent to
1)
2)
3)
4)
?
11 What are the roots of the equation
1)
2)
3)
4)
?
12 What are the solutions to the equation
1)
2)
3)
4)
?
13 Max solves a quadratic equation by completing the square. He shows a correct step:
What are the solutions to his equation?
1)
2)
3)
4)
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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Name: __________________________________
14 Solve
form.
by completing the square, expressing the result in simplest radical
15 A student was given the equation
first step that was written is shown below.
to solve by completing the square. The
The next step in the student’s process was
. State the value of c that
creates a perfect square trinomial. Explain how the value of c is determined.
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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1 ANS: 1
REF: 081527a2
2 ANS: 2
3 ANS: 2
REF: 061122a2
REF: 011116a2
4 ANS: 1
5 ANS: 3
REF: 061408a2
REF: 061505a2
6 ANS: 2
REF: 011614ai
7 ANS: 4
REF: 061518ai
8 ANS: 2
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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REF: 061408ai
9 ANS: 4
REF: 011517ai
10 ANS: 4
REF: 011607ai
11 ANS: 2
REF: 061410ai
12 ANS: 1
REF: 061523ai
13 ANS: 2
Regents Exam Questions CC.A.REI.4: Solving Quadratics 4
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REF: 011408a2
14 ANS:
.
REF: fall0936a2
15 ANS:
Since
REF: 081432ai
, p is half the coefficient of x, and the constant term is equal to
.