Algebra-1

Step 1: Find the points of intersection

To find the points where the parabola and the line intersect, we set the two equations equal to each other:

Rearranging the terms:

This is a quadratic equation of the form , where:

a = 2

b = -1

c = 2

 

Step 2: Analyze the discriminant

To determine the number of real solutions (which corresponds to the number of intersection points), we use the discriminant of the quadratic equation. The discriminant  is given by:

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