Systems of Inequalities Answers
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1
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Which point justifies the shaded area by satisfying ?
A
(12, 6)B
(–2, 6)C
(8, –6)D
(–1, –2)2
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Review the graph of a conic inequality.
A
x ≥ (y + 3)2 + 1B
x ≤ (y + 3)2 + 1C
x ≥ (y – 3)2 + 1D
x ≤ (y – 3)2 + 13
Consider a student’s work in determining the solution set of x > 2(y – 1)2 – 2.Test point: (2.25, 1.25) x > 2(y – 1)2 – 2 2.25 > 2(1.25 – 1)2 – 2 2.25 > 2(0.25)2 – 2 2.25 > 2(0.0625) – 2 2.25 > 0.125 – 2 2.25 > –1.875 Conclusion: The point (2.25, 1.25) satisfies the given inequality. Solution set:
A
There are no errors.B
The conclusion statement is incorrect.C
The graph of the solution set is incorrect.D
The substitution of x and y values is incorrect.4
Consider the graph of . Which point could confirm the graph is shaded correctly?
A
(–4, 2)B
(–3, 5)C
(–3, 1)D
(–2, 2)5
Review the graph of .
A
(–2, 4)B
(2, –12)C
(–1, –1)D
(–4, –10)6
Which graph represents the solution set of ?
A
On a coordinate plane, an ellipse has center (2, negative 4) and goes through (2, negative 2), (7, negative 4), (2, negative 6), and (negative 3, negative 4). Everything inside of the ellipse is shaded.
B
On a coordinate plane, an ellipse has center (2, negative 4) and goes through (2, negative 2), (7, negative 4), (2, negative 6), and (negative 3, negative 4). Everything outside of the ellipse is shaded.
C
On a coordinate plane, an ellipse has center (2, negative 4) and goes through (2, 1), (4, negative 4), (2, negative 9), and (0, negative 4). Everything outside of the ellipse is shaded.
D
On a coordinate plane, an ellipse has center (2, negative 4) and goes through (2, 1), (4, negative 4), (2, negative 9), and (0, negative 4). Everything inside of the ellipse is shaded.
7
Which graph represents ?
A
On a coordinate plane, one part of a conic graph goes through (8, 0), has a vertex at (2, negative 3), and goes through (10, negative 6). The other part goes through (negative 10, 0), has a vertex at (negative 4, negative 3), and goes through (negative 8, negative 5). Everything inside of the conic graph is shaded.
B
On a coordinate plane, one part of a conic graph goes through (8, 0), has a vertex at (2, negative 3), and goes through (10, negative 6). The other part goes through (negative 10, 0), has a vertex at (negative 4, negative 3), and goes through (negative 8, negative 5). Everything outside of the conic graph is shaded.
C
On a coordinate plane, a conic graph goes through (negative 6, 5), has a vertex at (negative 2, 3), and goes through (negative 8, 0). The other part goes through (12, 6), has a vertex at (4, 3), and goes through (10, 0). Everything outside of the conic graph is shaded.
D
On a coordinate plane, a conic graph goes through (negative 6, 5), has a vertex at (negative 2, 3), and goes through (negative 8, 0). The other part goes through (12, 6), has a vertex at (4, 3), and goes through (10, 0). Everything inside of the conic graph is shaded.
8
Which graph represents ?
A
On a coordinate plane, one part of a conic graph goes through (negative 8, 6), has a vertex at (negative 2, negative 1), and goes through (negative 7, negative 7). The other part goes through (11, 5), has a vertex at (6, negative 1), and goes through (11, negative 7). Everything outside of the conic graph is shaded.
B
On a coordinate plane, one part of a conic graph goes through (negative 8, 6), has a vertex at (negative 2, negative 1), and goes through (negative 7, negative 7). The other part goes through (11, 5), has a vertex at (6, negative 1), and goes through (11, negative 7). Everything inside of the conic graph is shaded.
C
On a coordinate plane, one part of a conic graph goes through (negative 3, 4), has a vertex at (negative 1, negative 1), and goes through (negative 3, negative 6). The other part goes through (10, 7), has a vertex at (5, negative 1), and goes through (7, negative 6). Everything outside of the conic graph is shaded.
D
On a coordinate plane, one part of a conic graph goes through (negative 3, 4), has a vertex at (negative 1, negative 1), and goes through (negative 3, negative 6). The other part goes through (10, 7), has a vertex at (5, negative 1), and goes through (7, negative 6). Everything inside of the conic graph is shaded.
9
Given x – 5 < (y – 8)2, which graph represents the inequality?
A
On a coordinate plane, a parabola opens up. It goes through (0, 20), has a vertex at (8, 5), and goes through (14, 14). Everything outside and below the parabola is shaded.
B
On a coordinate plane, a parabola opens down. It goes through (0, negative 10), has vertex (3, 5), and goes through (14, negative 4). Everything inside and below the parabola is shaded.
C
On a coordinate plane, a parabola opens to the right. It goes through (21, 16), has vertex (3, 8) and goes through (22, 0). Everything outside and to the left of the parabola is shaded.
D
On a coordinate plane, a parabola opens to the left. It goes through (negative 8, 15), has vertex (5, 8), and goes through (negative 10, 0).
10
Which point justifies the shaded area by satisfying ?
A
(1, 1)B
(4, 1)C
(–1, 2)D
(2, –2)Did you find these answers helpful?
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