Regents Exam Questions A.REI.B.4: Solving Quadratics 5
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15 When directed to solve a quadratic equation by
completing the square, Sam arrived at the equation
ÊÁ
ˆ2
ÁÁ x  5 ˜˜˜  13 . Which equation could have been
ÁÁ
2 ˜˜¯
4
Ë
11 What are the solutions to the equation x 2  8x  10?
1) 4  10
2)
3)
4)
4  26
4  10
4  26
the original equation given to Sam?
1) x 2  5x  7  0
2) x 2  5x  3  0
3) x 2  5x  7  0
4) x 2  5x  3  0
12 What are the solutions to the equation x 2  8x  24?
1) x  4  2 10
2)
3)
4)
x  4  2 10
x  42 2
x  4  2 2
13 Which value of k will make x 2 
16 Solve the following equation by completing the
square: x 2  4x  2
1
x  k a perfect
4
17 Solve the equation x 2  6x  15 by completing the
square.
square trinomial?
1
1)
64
1
2)
16
1
3)
8
1
4)
4
18 Use the method of completing the square to
determine the exact values of x for the equation
x 2  8x  6  0 .
19 Find the exact roots of x 2  10x  8  0 by
completing the square.
14 Brian correctly used a method of completing the
square to solve the equation x 2  7x  11  0.
Brian’s first step was to rewrite the equation as
x 2  7x  11 . He then added a number to both sides
of the equation. Which number did he add?
7
1)
2
49
2)
4
49
3)
2
4) 49
20 Solve 2x 2  12x  4  0 by completing the square,
expressing the result in simplest radical form.
21 A student was given the equation x 2  6x  13  0
to solve by completing the square. The first step
that was written is shown below.
x 2  6x  13
The next step in the student’s process was
x 2  6x  c  13  c . State the value of c that
creates a perfect square trinomial. Explain how the
value of c is determined.
2