3.8 Linear -Quadratic Systems

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

Linear – Quadratic Systems

Linear-Quadratic Systems

EXAMPLE 1 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) = -4.9t2 + 5500 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 + 4500 t is time in seconds h(t) is the height above the ground, in metres

EXAMPLE 1 pg 194 free fall h(t) = -4.9t2 + 5500 parachute released h(t) = -5t + 4500 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.

EXAMPLE 1 pg 194 At the moment that the parachute is opened, the height represented by each equation must be the same.

EXAMPLE 1 pg 194 According to the models, Josh will open his parachute at 14.8s.

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.

EXAMPLE 1 pg 194 Graphing 

EXAMPLE 2 pg197 Determine the number of points of intersection of the following two functions.

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

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

EXAMPLE 3

EXAMPLE 4

EXAMPLE 5

In Summary

HomeFUN  pg 198-199 # 1a, 2bc, 3, 5, 6, 8, 9, 10, 11, 12, 14 # 1a (graph by hand, check your answer with Desmos),