1. Grade 11 University: (MCR3U) Unit 1: Algebra & Quadratic Functions Intersection of Linear and Non-linear Relations
Mr. Choi
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2. A linear-quadratic system can be solved algebraically by a method we used for solving linear systems. The linear equation is solved for either variable, and the expression obtained substituted in the quadratic equation. A linear relation and a non-linear relation can intersect at zero, one, or two points. A linear-quadratic system of equations can have no solution, one solution, or two solutions.
Intersection of Linear and Non-linear Relations
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3. Example 1: Finding Points of Intersection of a Line and a Circle
Find the coordinates of the points of intersection to the line
and the circle
. a) graphically b) algebraically
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

4. Example 2: Finding Points of Intersection of a Line and a Parabola
Find the coordinates of the points of intersection of the parabola
and the line
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

5. Example 3: Finding Points of Intersection of a Line and a Reciprocal Function
Find the coordinates of the points of intersection of the reciprocal function
and the line
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

6. Example 4: Problem Solving
A sky diver jumped from an airplane and fell freely for several seconds before releasing her parachute. Her height, h, in metres, above the ground at any time is given by:
before she released her parachute, and
after she released the parachute.
a) How long after jumping did she release her parachute?
b) How high was she above the ground at that time?
c) If the parachute released, when will the sky diver landed on the ground?
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

7. Example 4: Problem Solving (Continued)
A sky diver jumped from an airplane and fell freely for several seconds before releasing her parachute. Her height, h, in metres, above the ground at any time is given by:
before she released her parachute, and
after she released the parachute.
a) How long after jumping did she release her parachute?
b) How high was she above the ground at that time?
c) If the parachute released, when will the sky diver landed on the ground?
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

8. Homework
Work sheet: Intersection of Linear and Non-Linear Relations (All) Text: P. 68 #1,3,5bc,10,11,13 Check the website for updates
Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved

9. End of lesson Intersection of Linear and Non-linear Relations
© 2017 E. Choi – MCR3U - All Rights Reserved