1. 3.8 Linear -Quadratic Systems

2. What happens when a line meets a parabola?
Show me a sketch!!

3. Linear – Quadratic Systems

4. Linear-Quadratic Systems

5. EXAMPLE pg 194
Josh has decided to celebrate his birthday by going skydiving. He loves to freefall, so he will wait for some time before opening his parachute.
His height after jumping from the airplane before he opens his parachute is modelled by the quadratic function h(t) = -4.9t
After he releases his parachute, he begins falling at a constant rate. His height above the ground is modelled by the linear function h(t) = -5t
t is time in seconds
h(t) is the height above the ground, in metres

6. EXAMPLE 1 pg 194 free fall h(t) = -4.9t2 + 5500
parachute released h(t) = -5t
According to these models, how long after jumping out of the airplane did Josh release his parachute?
At what height did this occur?
At the moment that the parachute is opened, the height
represented by each equation must be the same.

7. EXAMPLE pg 194
At the moment that the parachute is opened, the height
represented by each equation must be the same.

8. EXAMPLE pg 194
According to the models, Josh will open his parachute at 14.8s.

9. EXAMPLE 1 pg 194 Now let’s determine the height at which he opened his
parachute.
Josh opened his parachute at a height of
4426m above the ground.

10. EXAMPLE pg 194 Graphing 

11. EXAMPLE pg197
Determine the number of points of intersection of the following two functions.

12. EXAMPLE 2
Determine the number of points of intersection of the following two functions.

13. EXAMPLE 2
Determine the number of points of intersection of the following two functions.

14. EXAMPLE 3

15. EXAMPLE 4

16. EXAMPLE 5

17. In Summary

18. HomeFUN 
pg # 1a, 2bc, 3, 5, 6, 8, 9, 10, 11, 12, 14 # 1a (graph by hand, check your answer with Desmos),