This week I learned about solving quadratic systems of equations.

A linear-quadratic system can have 3 possible solutions:

1) 2 solutions (line intersects parabola at 2 points)

2) 1 solution (Line intersects parabola at 1 point)

3) 0 solutions (line doesn’t intersect parabola)

A quadratic-quadratic system could have 4 possible solutions:

1) 2 solutions (parabolas intersect at 2 points)

2) 1 solution (parabolas intersect at 1 point)

3) 0 solutions (parabolas don’t intersect)

4) infinite solutions (parabolas are on top of one another)

How to solve a quadratic-quadratic system graphically:

Step one: Identify clues from the equations

Step two: graph the equations

Step three: Identify the intersects

The parabolas have 2 solutions (-2,-2) and (2,-2)