CPA2 - 3.6 Quadratic Inequalities

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0, ax² + bx + c > 0, ax² + bx + c ≤ 0, or ax² + bx + c ≥ 0.

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 not on the boundary.

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 on the other side of the inequality.

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 on the other side of the inequality.

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 on the other side of the inequality.

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 on the other side of the inequality.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the significance of the direction of a parabola in quadratic inequalities?

Back

The direction of a parabola (upward or downward) determines whether the solutions to the inequality are above or below the parabola.

Front

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

Back

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