Lesson 6

Using Algebra to Solve Problems Modelled by Systems Involving Quadratic Equations

 

In the previous lesson you modelled problems with systems of linear-quadratic equations and quadratic-quadratic equations. You solved those problems graphically. In the final section of this lesson, you will continue to develop your skills in modelling problems with systems. You will, however, focus on solving the problems algebraically.

 

Try This 4

 

The August long weekend in Edmonton always marks the celebration of Heritage Festival. The annual event showcases the food, culture, and wares of many countries, ranging from Afghanistan to Zimbabwe. In preparation for the event, approximately 65 pavilions are raised all over the 150-ac Hawrelak Park.

 

Assume that some of the pavilions in Hawrelak Park are arranged in the shape of a parabola, as shown in the following diagram.

 

 

The parabola is described by the equation y = 0.003x2 + 0.005x. A path described by the equation y = 0.08x + 105 connects two food ticket kiosks, which are represented by red pentagons in the diagram. In both cases, x represents the horizontal distance (in metres) from the entrance and y represents the vertical distance (in metres) from the entrance.

1. Determine the coordinates of the two kiosks.
   
   
2. What is the length of the path between the two kiosks?

Save your work in your course folder.

 

You will need to retrieve your work later in the lesson for review with a partner.