Algebra II : Quadratic Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #8 : Graphing Hyperbolic Inequalities

Which inequality does this graph represent?

Screen shot 2020 08 26 at 8.59.20 am

Possible Answers:

Correct answer:

Explanation:

The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is . In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The graph shows a vertical hyperbola, so in its corresponding inequality the y-term must appear first. The center is (0, 0), so neither x nor y can be followed by a constant. The center is shaded, so the left side of the graph’s corresponding inequality (the side containing the variables x and y) is less than the constant on the right side. The lines are solid rather than dashed, so the inequality sign must be  rather than .

Example Question #9 : Graphing Hyperbolic Inequalities

Which graph represents the inequality ?

Possible Answers:

Screen shot 2020 08 26 at 8.44.31 am

Screen shot 2020 08 26 at 8.46.33 am

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Screen shot 2020 08 26 at 8.43.13 am

Correct answer:

Screen shot 2020 08 26 at 8.43.13 am

Explanation:

The equation for a horizontal hyperbola is. The equation for a vertical hyperbola is . In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. Neither the x nor the y in the inequality are followed by constants, so the graph must be centered on (0,0). The x-term appears first, so the graph must show a horizontal hyperbola. The inequality sign is  rather than , so the lines must be dashed rather than solid. The left side is less than rather than greater than the constant, so the center must be shaded.

Example Question #10 : Graphing Hyperbolic Inequalities

Which graph represents the inequality ?

Possible Answers:

Screen shot 2020 08 26 at 8.33.13 am

Screen shot 2020 08 26 at 8.35.55 am

Screen shot 2020 08 26 at 8.34.53 am

Screen shot 2020 08 26 at 8.36.21 am

Correct answer:

Screen shot 2020 08 26 at 8.33.13 am

Explanation:

The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is . In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The x and y in the inequality are followed by the constants 2 and -1 respectively, so the graph must be centered on (-2, 1). The y-term appears first, so the graph must show a vertical hyperbola. The inequality sign is  rather than , so the lines must be solid rather than dashed. The left side is greater than rather than less than the constant, so the center must not be shaded.

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