Predicting Possible Collisions Using Nonlinear Equations

This lesson teaches how to write and solve systems of nonlinear equations using graphs of quadratic equations. It covers the basics of quadratic equations, including circles, ellipses, parabolas, and hyperbolas. The lesson uses a real-world scenario involving a tour boat and a fishing boat to illustrate the application of these equations. The tour boat follows an elliptical path, while the fishing boat follows a parabolic path. By graphing these paths, the lesson assesses the risk of collision between the boats, identifying potential collision points. The lesson concludes with a review of the key concepts and equations used.

Which of the following is NOT a type of quadratic equation discussed in the lesson?

• Parabola

• Triangle

• Circle

• Ellipse

What is the initial direction the tour boat travels from the island?

• West

• South

• East

• North

How far is the tour boat from the island on the east and west sides during its elliptical path?

• Half a mile

• 6/10 of a mile

• 1 mile

• 3/10 of a mile

What is the vertex of the parabolic path taken by the fishing boat?

• (0, 0)

• (3/10, 0)

• (1, 5/10)

• (0, 3/10)

What does the negative number in the intersection point indicate in the context of the boat paths?

• A collision point to the east of the island

• A collision point to the west of the island

• No collision risk

• A collision point to the north of the island