Solve a quadratic inequality by graphing the related quadratic function.
After completing this tutorial, you will be able to complete the following:
Solving a linear inequality is pretty easy. It is a big step from there to solving quadratic inequalities. We first introduce the following six conditions to show all the possible cases of quadratic functions and the x-values where the function is positive, negative, or zero.
Apply the conditions to the parabola
The following parabola opens downward, has two x-intercepts, and the vertex is above the x-axis. The function is positive between the x-intercepts; see the left graphic where f(x) > 0: -5 < x < -1. For the rest of the coordinate plane the function is negative; see the right graphic where f(x) < 0: x < -5 or x > -1.
To solve a quadratic inequality by graphingTo solve a quadratic inequality means to determine the x-values which satisfy the given inequality. We can solve a quadratic inequality by graphing its related function. Once we sketched the related parabola, we just need to look at the x-values for which the related function lies above, below or on the x-axis depending in the inequality symbol
|Approximate Time||30 Minutes|
|Pre-requisite Concepts||coordinate plane, discriminant, graphing quadratic functions, linear inequalities, parabola, quadratic function, vertex, x-intercepts|
|Type of Tutorial||Guided Discovery|
|Key Vocabulary||graphing quadratic functions, graphs, inequalities|