What is the significance of testing points in quadratic inequalities?

Testing points helps to determine which regions of the graph satisfy the inequality, allowing for the identification of the solution set.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What does it mean for a quadratic inequality to be 'greater than' or 'less than'?

'Greater than' means the values of $$y$$ are above the parabola, while 'less than' means the values of $$y$$ are below the parabola.

What is the role of the discriminant in quadratic equations?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation. If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

How can you identify the direction of a parabola?

The direction of a parabola is determined by the sign of the coefficient $$a$$ in the standard form $$y = ax^2 + bx + c$$ . If $$a > 0$$ , the parabola opens upwards; if $$a

What is the importance of the roots of a quadratic equation in relation to inequalities?

The roots of a quadratic equation are the x-values where the graph intersects the x-axis. They help to determine the intervals to test for the solution of the inequality.

What does it mean for a quadratic inequality to have 'no solution'?

A quadratic inequality has 'no solution' if there are no values of $$x$$ that satisfy the inequality, often occurring when the parabola is entirely above or below the x-axis.

How do you solve a quadratic inequality algebraically?

To solve a quadratic inequality algebraically, first solve the corresponding quadratic equation to find the roots, then test intervals between the roots to see where the inequality holds true.

Quadratic Inequality (Period 7) Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic inequality?

Back

2.

FLASHCARD QUESTION

Front

How do you determine the solution area for a quadratic inequality?

Back

To determine the solution area, you can test points in the regions defined by the parabola. If the test point satisfies the inequality, that region is part of the solution.

3.

FLASHCARD QUESTION

Front

What does it mean if a solution area is 'shaded' in a graph of a quadratic inequality?

Back

4.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What does the term 'non-shaded area' refer to in the context of quadratic inequalities?

Back

The non-shaded area refers to the regions of the graph that do not satisfy the inequality, meaning points in this area do not fulfill the condition set by the inequality.

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