Quadratic functions are written as ( f(x) = ax^2 + bx + c ). When we graph them, we see a shape called a parabola.
Here’s a simpler breakdown:
Inequalities: Quadratic inequalities, like ( ax^2 + bx + c < 0 ), show areas where the function's value is below a certain number.
Roots: The roots are the points where the graph crosses the x-axis. We can find these points using the formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
Graph Interpretation: By looking at how the parabola opens, we can tell a lot. If ( a > 0 ), the parabola opens upward. If ( a < 0 ), it opens downward. This helps us understand the solutions better.
Solution Regions: The solutions usually come in groups based on the roots. These groups help us see what the inequality means.
In summary, quadratic functions and their inequalities can give us a lot of information about their graphs and solutions!
Quadratic functions are written as ( f(x) = ax^2 + bx + c ). When we graph them, we see a shape called a parabola.
Here’s a simpler breakdown:
Inequalities: Quadratic inequalities, like ( ax^2 + bx + c < 0 ), show areas where the function's value is below a certain number.
Roots: The roots are the points where the graph crosses the x-axis. We can find these points using the formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
Graph Interpretation: By looking at how the parabola opens, we can tell a lot. If ( a > 0 ), the parabola opens upward. If ( a < 0 ), it opens downward. This helps us understand the solutions better.
Solution Regions: The solutions usually come in groups based on the roots. These groups help us see what the inequality means.
In summary, quadratic functions and their inequalities can give us a lot of information about their graphs and solutions!