Graphing Quadratic Inequalities

Front

What is a quadratic inequality?

Back

Front

How do you graph a quadratic inequality?

Back

To graph a quadratic inequality, first graph the corresponding quadratic equation as a boundary line. Then, determine which side of the parabola satisfies the inequality by testing a point.

Front

What does the symbol '<' indicate in a quadratic inequality?

Back

The symbol '<' indicates that the values of the quadratic expression are less than the value of 'y', meaning the region below the parabola is included in the solution.

Front

What does the symbol '>' indicate in a quadratic inequality?

Back

The symbol '>' indicates that the values of the quadratic expression are greater than the value of 'y', meaning the region above the parabola is included in the solution.

Front

What does the symbol '≤' indicate in a quadratic inequality?

Back

The symbol '≤' indicates that the values of the quadratic expression are less than or equal to the value of 'y', meaning the region below the parabola, including the parabola itself, is included in the solution.

Front

What does the symbol '≥' indicate in a quadratic inequality?

Back

The symbol '≥' indicates that the values of the quadratic expression are greater than or equal to the value of 'y', meaning the region above the parabola, including the parabola itself, is included in the solution.

Front

What is the vertex of a parabola represented by a quadratic function?

Back

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set the quadratic equation equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the significance of the direction of a parabola?

Back

The direction of a parabola (opening upwards or downwards) is determined by the coefficient 'a' in the quadratic equation. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities ('<' and '>') do not include the boundary line, while non-strict inequalities ('≤' and '≥') include the boundary line in the solution set.