AnswersAlgebra III ASolving Quadratic Equations: Completing the Square

Solving Linear-Quadratic Systems Answers

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The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

Question illustration
A
(4, 4)
B
(–4, –12)
C
(4, 4) and (–4, 12)
D
(–4, 4) and (4, 12)
4

Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2?

Question illustration
A
(–2, 0) and (0, 1)
B
(0, –2) and (1, 0)
C
(–2, 0) and (1, 0)
D
(0, –2) and (0, 1)
10

Which parabola will have one real solution with the line y = x – 5?

Question illustration
A
y = x2 + x – 4
B
y = x2 + 2x – 1
C
y = x2 + 6x + 9
D
y = x2 + 7x + 4
11

Which graph shows a system of equations with a solution at (–1, 1)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?

Question illustration
A
(1, 0) and (0, –1)
B
(–2, –3) and (1, 0)
C
(0, –3) and (1, 0)
D
(–3, –2) and (0, 1)
13

Which line will have no solution with the parabola y – x + 2 = x2?

Question illustration
A
y = –3x –3
B
y = –2x –3
C
y = 2x –3
D
y = 3x –3
14

Which represents the solution(s) of the system of equations, y = x2 – 4x – 21 and y = –5x – 22? Determine the solution set algebraically.

A
(–1, –17)
B
(1, –27)
C
(–1, –17) and (1, –27)
D
no solutions
15

Which graph most likely shows a system of equations with no solutions?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.

A
(3, 25)
B
(–3, 49)
C
(3, 25) and (7, 9)
D
(–3, 49) and (–7, 65)
17

Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2?

Question illustration
A
(–2, 0) and (0, 1)
B
(0, –2) and (1, 0)
C
(–2, 0) and (1, 0)
D
(0, –2) and (0, 1)
18

The first three steps in determining the solution set of the system of equations algebraically are shown.y = x2 − x − 3 y = −3x + 5

Question illustration
A
(−2, −1) and (4, 17)
B
(−2, 11) and (4, −7)
C
(2, −1) and (−4, 17)
D
(2, 11) and (−4, −7)
19

The first three steps in determining the solution set of the system of equations algebraically are shown.y = x2 − x − 3 y = −3x + 5

Question illustration
A
(−2, −1) and (4, 17)
B
(−2, 11) and (4, −7)
C
(2, −1) and (−4, 17)
D
(2, 11) and (−4, −7)

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