(b) The points of intersection of the curves are the solutions of:
f (x) = g (x) 2 x = 2x + 1 2 x – 2x –1 = 0
Using the graph, the solutions to 2 x – 2x –1 = 0 are x = 0 and x = 2·6.
8 y
7 5·6
5 6
3 4
2 1
2·3 0 EXAMPLE 6 A missile is fi red from a point A. Its height, in tens of metres above the ground, t seconds after being fi red, is
given by h1 = 2 t , t ≥ 0. The instant it is fi red, another missile is fi red from a drone at point B. Its height h2, in tens of metres above the ground, t seconds after being fi red, is given by h2 = 10 − t 2 , t ≥ 0. (a) Find the initial height of each missile above the ground.
(b) Use the table below to plot graphs of h1 and h2 against t on graph paper. t
h 1 h 2
(c) Use your graph to estimate when the missiles collide and how high above the ground the collision occurs. 283 0 0·5 1 1·5 2 2·5 3 0·5 1 1·5 2 2·5 2·6 3 x
