The expression under the radical in the quadratic formula is called the discriminant. The discriminant helps you determine the number of solutions of a quadratic equation. Solve the following problems. Click “Submit” when finished.

Look at the graph of the quadratic equation <EQUATION>. The <EQUATION> intercepts of this parabola are <EQUATION> and <EQUATION>. The <EQUATION> coordinate of each <EQUATION> intercept is zero, so finding the <EQUATION> intercepts is the same as finding the places where <EQUATION>. That is, the <EQUATION> intercepts are the solutions of <EQUATION>. To solve this equation, you can either factor or use the quadratic formula.

Using the quadratic formula, we find that the equation has two solutions, <EQUATION> and <EQUATION>. These values agree with the <EQUATION> coordinates of the <EQUATION> intercepts. Notice that in this case the discriminant is positive, so the quadratic equation has two real-number solutions. The solutions of the quadratic equation correspond to the <EQUATION> intercepts of the parabola, so this confirms that the parabola has two <EQUATION> intercepts.

Use the sliders to change the values of <EQUATION>, <EQUATION>, and <EQUATION> in the equation <EQUATION>. Notice how the value of the discriminant affects the number of <EQUATION> intercepts of the parabola. Click “Done Exploring” when finished.

The parabola has two <EQUATION> intercepts if the discriminant of its equation is positive, one <EQUATION> intercept if the discriminant is zero, and no <EQUATION> intercepts if the discriminant is negative.

Match each graph with the discriminant of the quadratic equation it represents. Click “Submit” when finished.

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