Algebra 9

3 marks · Normal

The graphs of y = x + 2 and y = x^2 – 2x are shown below.

Calculate the x-coordinates of the points where the graphs intersect.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

x = 1\text{ or }x = -2

Also accept: x = -2 and x = 1

Common mistakes: Sign error in rearranging; Missing one root

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Equates x+2 = x^2 - 2x or equivalent.

M2 · 1 mark · Rearranges and simplifies correctly to x^2 - 3x - 2 = 0 and attempts to solve the quadratic equation.

A1 · 1 mark · Gives both correct solutions: x = 1 and x = -2.

Worked solution

Equate the equations to find points of intersection:

Bring all terms to one side:

Factorise:

So x = 2 or x = -1.