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You have now learned how to solve linear-quadratic systems of equations.

You know that the solution, or solutions, to a linear-quadratic system occur(s) where the graphs of the equations intersect.

You have seen that the graph of a linear equation and a quadratic equation can intersect at 0, 1 or 2 places.

What if we were working with a system of equations containing two quadratic equations or a quadratic-quadratic system.

In how many ways could the graphs of two quadratic equations intersect?

Use the below action figure to explore the ways in which two quadratic equations can intersect. When finished, use the question box below to check your understanding.

Note that sometimes an intersection will occur where two curves are tangent. Due to the restrictions of the action figure, it will appear that the curves touch at more than one point. Keep in mind that this is not the case.