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SOLVING EQUATIONS Menu

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As explored before, there are various ways that the graphs of equations can intersect.

You have seen that it is possible for linear-quadratic systems of equations to intersect at 0, 1 or 2 points, and quadratic-quadratic systems of equations to intersect at 0, 1, 2, 3 or 4 points.

Have you noticed that you can change the number of intersection points between the graphs of two equations by transforming one of the curves?

As you vary the coefficients in the standard equation of one of the curves, the graph of the curve is transformed.

As the graph being transformed moves over a fixed graph, the intersection points between the two curves vary.

Use the action figure below to explore how the transformation of graph over a fixed graph affects the number of intersection points between the two graphs. You will be able to transform the graph of a circle or an ellipse over the fixed graph of a line, circle, or and ellipse.

When finished, answer the questions in the question box to check your understanding of transformations and intersection.

Good work! You have completed the module on solving systems of equations. The foward-button below will take you back to the Solving Equations Menu where you can choose to write the Quiz, to review the Goals and Objectives of this module to see if you covered everything, or to return to the Main Menu and carry on with the next module.