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Points of intersection ​

Notes ​

In the picture below, A and B are points of intersection between

y=x+2

and

y=x2−2x+2

intersecting line and parabola

Notice that there could be either 2,1 or 0 points of intersection depending on the position of the line.

When there is only one point of intersection, we say that the line is a tangent to the parabola:

tangent to parabola

We're going to learn to find points of intersection, and solve problems about points of intersection.

Example ​

Find the points of intersection between the line

y=−4x−1

and the parabola

y=7−x2

Exercise ​