Quadratic inequalities are similar to quadratic equations, but there's a twist!

Quadratic equations, like ( ax^2 + bx + c = 0 ), give you specific values of ( x ).

On the other hand, quadratic inequalities tell you when one expression is less than, greater than, or equal to another expression.

For example, you might see something like ( x^2 - 5x + 6 < 0 ). Instead of just finding a single value for ( x ), you’re looking for all the values that make this statement true.

Key Differences:

1. Outcome:

   • Equations: Give exact answers (like ( x = 2 ), ( x = 3 )).
   • Inequalities: Provide a range of values (like ( x < 2 ) or ( x > 3 )).

2. Graphing:

   • Equations show where a curve (like a parabola) touches the x-axis.
   • Inequalities show sections above or below that curve. These sections show where the values are true based on the inequality.

3. Solving Methods:

   • You can solve both by factoring, completing the square, or using the quadratic formula.
   • But for inequalities, you often check different intervals created by the roots of the equation.

Understanding these differences will make it easier to solve problems and read graphs. These skills are very important as you continue learning math!