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## How Two Parabolas Intersect

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### Lesson Focus

#### How Two Parabolas Intersect

Algebra-1

You will find the intersection points of two parabolas to determine the set of x-values for which one parabola lies above the other.

### Now You Know

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

• Determine how many points two parabolas intersect at.
• Find the intersection points of two parabolas.
• Find the set of x–values for which one parabola lies above the other.

### Everything You'll Have Covered

Parabola and line intersections

Before considering how two parabolas intersect, remember how a parabola and line may intersect at one point, two points, or no points.

The main thing to remember is to equalize the equation of the quadratic function and the linear equation to each other and then solve the derived quadratic equations to find the intersection points, if any. Three examples are shown in the following table:

Intersections of two parabolas

To determine if there are one, two, or no intersection points of two parabolas, you can make the two functions equal to each other. This time, you can get either a linear equation or a quadratic equation. In each case, you need to solve the equation to find the intersection points.

When the derived equation from two quadratic functions is also a quadratic, you can't solve for x. The next table describes how to use the discriminant to determine the number of intersection points.

Discriminant used to determine the number of intersection point of two parabolas

The set of x-values for which f(x) is above or below g(x)

### Tutorial Details

 Approximate Time 30 Minutes Pre-requisite Concepts Students should understand the concepts of discriminant, graph a quadratic, orientation of a parabola, parabola, quadratic, quadratic function, root, and zeros of a quadratic function. Course Algebra-1 Type of Tutorial Guided Discovery Key Vocabulary parabola, intersection points, x-values