Questions and Answers
What is the definition of Quadratic Inequalities?
What are the steps to graph a quadratic inequality?
1.) Graph the function 2.) Test a point 3.) If point is a solution shade area that includes the point/If point isn't a solution shade area that doesn't include the point.
How can quadratic inequalities in one variable be solved?
By using the graphs of the related quadratic functions.
To solve $ax² + bx + c < 0$ by graphing, first _____ the graph.
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To solve a quadratic inequality algebraically, you would typically manipulate the ______ equation.
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Study Notes
Quadratic Inequalities
- Quadratic inequalities can be graphed in two variables using techniques similar to those for linear inequalities.
- The graph of a quadratic inequality represents regions where the inequality holds true.
Graphing a Quadratic Inequality
- Begin by graphing the corresponding quadratic function.
- Choose a test point that is not on the graph to determine the solution region.
- If the test point satisfies the inequality, shade the area that includes the point; otherwise, shade the area that does not include the point.
Solving Quadratic Inequalities
- Quadratic inequalities in one variable can be addressed through the graphs of related quadratic functions.
- The x-intercepts of the quadratic function indicate potential boundaries for shading the solution regions.
Solving ax² + bx + c < 0 by Graphing
- Graph the corresponding quadratic function and identify areas below the x-axis.
- The regions where the quadratic function is negative correspond to the solutions of the inequality.
Solving a Quadratic Inequality Algebraically
- Algebraic methods involve rewriting the inequality and finding critical points where the equality holds.
- Analyze intervals between critical points to determine where the inequality is satisfied.
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Description
Explore the key concepts of quadratic inequalities with this flashcard set. Each card provides definitions and methods for graphing quadratic inequalities. Perfect for studying and enhancing your understanding of this important algebra topic.
