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.

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, meaning the region above the parabola is included.

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, meaning the region above the parabola and the parabola itself are included.

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, meaning the region below the parabola is included.

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, meaning the region below the parabola and the parabola itself are included.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point of the parabola, 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 axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.