4. Points of intersection

to find the points of intersection of two graphs

• plot the graphs on the same axes

or

• equivalise the functions

  • f(x) = g(x)

  • (x + 1)(x + 2) = x(x +1)

  • x² + 3x + 2 = x² + x

• equivalise the functions to 0

  • 2x + 2 = 0

• solve/factorise to find the x value(s)

  • x = -1

• substitute the x value(s) into one of the functions to find the y value(s)

  • (-1)(-1 + 1) = 0

  • y = 0

• point of intersection = (0, -1)

the number of points of intersection are the number of real solutions to the functions equal to zero

• (x + 1)(x + 2) = x(x +1) → one intersection

• 2x + 2 = 0 → one real solution