Quadratic Inequality Explanation:

Quadratic inequalities involve quadratic expressions with inequalities such as greater than (>), greater than or equal to (≥), less than (<), or="" less="" than="" or="" equal="" to="" (≤).="" the="" given="" inequality="" ax^2="" +="" bx="" +="" c=""> 0 is a quadratic inequality because it contains a quadratic expression (ax^2 + bx + c) and the inequality symbol (>).

Characteristics of Quadratic Inequalities:
- Quadratic inequalities involve a quadratic expression.
- The solutions to quadratic inequalities are represented as intervals on a number line.
- The inequality symbol determines whether the solutions are above or below the x-axis.

Graphical Representation:
When graphed on a coordinate plane, the quadratic expression ax^2 + bx + c represents a parabola. The inequality ax^2 + bx + c > 0 indicates that the quadratic expression is positive, which means the graph of the parabola is above the x-axis.

Solving Quadratic Inequalities:
To solve the quadratic inequality ax^2 + bx + c > 0, one can use methods such as factoring, graphing, or the sign analysis method. The solutions will be represented as intervals on the number line where the quadratic expression is greater than zero.

Conclusion:
In conclusion, the given inequality ax^2 + bx + c > 0 is classified as a quadratic inequality because it involves a quadratic expression with an inequality symbol. Understanding quadratic inequalities is crucial in solving mathematical problems and analyzing relationships between variables.