Grade 11 University: (MCR3U) Unit 1: Algebra & Quadratic Functions Intersection of Linear and Non-linear Relations Mr. Choi © 2017 E. Choi – MCR3U - All Rights Reserved

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 © 2017 E. Choi – MCR3U - All Rights Reserved

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

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

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

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

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

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

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