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Solving Quadratic Inequalities by Graphing

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Solving Quadratic Inequalities by Graphing

Algebra-2

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Solve a quadratic inequality by graphing the related quadratic function.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Describe the x-values where the quadratic function is positive, negative or zero.
  • Solve a quadratic inequality by graphing the related quadratic function.

Everything You'll Have Covered

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

  • If we have f(x) < 0: The solution consists of the x-values for which the related function lies below the x-axis
  • If we have f(x) ? 0: The solution consists of the x-values for which the related function lies on or above the x-axis.

Tutorial Details

Approximate Time 30 Minutes
Pre-requisite Concepts coordinate plane, discriminant, graphing quadratic functions, linear inequalities, parabola, quadratic function, vertex, x-intercepts
Course Algebra-2
Type of Tutorial Guided Discovery
Key Vocabulary graphing quadratic functions, graphs, inequalities