AnswersCommon Core Algebra I 2014 - MA3109 B-CRSolving Quadratic Equations: Completing the Square

Solving Quadratic Equations: Completing the Square — Unit test Answers

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41
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What is the solution to 2x2+8x=x2-16?

A
x=-4
B
x=-2
C
x=2
D
x=4
42
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A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?

A
l(l – 2) = 168
B
l(l + 2) = 168
C
2l 2 = 168
D
l 2 = 168
Option D
43

Which equation results from taking the square root of both sides of (x – 9)2 = 81?

A
x – 9 = ±9
B
x + 9 = ±9
C
x + 3 = ±9
D
x – 3 = ±9
44

The product of two consecutive integers is 420. Which quadratic equation can be used to find x, the lesser number?

A
x2 + 1 = 420
B
x2 + 2 = 420
C
x2 + x = 420
D
x2 + 2x = 420
45

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.Quadratic formula: x = Substitution:

Question illustration
A
The –5 should be 5.
B
The 52 should be –52.
C
The 2 in the numerator should be –2.
D
The 2 in the denominator should be –2.
46

Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.

Question illustration
A
q = 5
Option A
B
q = -5
Option B
C
q = 3
Option C
D
q = -3
Option D
E
q = 25
Option E
47

Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.

A
(1, 1)
B
(0, 1) and (1, 1)
C
(0, 0) and (1, 1)
D
no solutions
48

Which represents the solution(s) of the system of equations, y = x2 – 6x + 8 and y = –x + 4? Determine the solution set by graphing.

A
(1, 3) only
B
(2, 0) and (4, 0)
C
(1, 3) and (4, 0)
D
no solutions
49

Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?Quadratic formula: x =

Question illustration
A
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option A
B
x = StartFraction negative 1 plus or minus StartRoot 1 squared minus 4 (negative 1)(negative 4) EndRoot Over 2(negative 1) EndFraction
Option B
C
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option C
D
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 2) EndRoot Over 2(1) EndFraction
Option D

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