Question

The sketch shows the graphs of:

y=2x + 2
y=2x^2 + 3x - 4

Work out the x-coordinates of the points S and T

Answer 1

Since both expressions in x are equal to y we can write:-

2x + 2 = 2x^2 + 3x - 4

2x^2 + x - 6 = 0

2x^2 + 4x - 3x - 6 = 0

2x(x + 2) - 3(x + 2) = 0

(2x - 3)(x + 2) = 0

x = 1.5 , -2

x coordinate of S = -2 and x coordinate of T = 1.5.