5.4 Graphing Quadratic Inequalities (in 2 Variables)

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 <, >, ≤, or ≥ 0.

Front

What does the graph of a quadratic inequality represent?

Back

The graph of a quadratic inequality represents the set of all points (x, y) that satisfy the inequality.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on its orientation.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the leading coefficient (a) in the quadratic expression: if a > 0, it opens upwards; if a < 0, it opens downwards.

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 formula x = -b/(2a).

Front

What does it mean for a region to be shaded in a graph of a quadratic inequality?

Back

Shaded regions indicate the set of solutions that satisfy the inequality, while non-shaded regions do not.

Front

How do you test if a point is a solution to a quadratic inequality?

Back

To test if a point (x, y) is a solution, substitute the x-value into the inequality and check if the resulting y-value satisfies the inequality.

Front

What is the significance of the shaded area in a system of inequalities?

Back

The shaded area in a system of inequalities represents all the points that satisfy all inequalities in the system.

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 specified value, meaning the region above the parabola is shaded.

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 specified value, meaning the region below the parabola is shaded.