Unit 5
4 marks · Normal5. The quadratic graph y = x^2 − 4x + 3 is transformed by a translation to obtain y = (x − 2)^2 − 4x + 3.
The x-intercepts are shown as points A and B.
Find the coordinates of A and B.
Describe the translation that maps the original graph to the transformed graph.
Write down the equation of the axis of symmetry of the original quadratic.
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
(a) A: (3, 0), B: (1, 0)
(b) A translation 2 units right
(c) x = 2
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets x^2 − 4x + 3 = 0 and attempts to solve
A1 (a) · 1 mark · States roots (3,0) and (1,0)
B1 (b) · 1 mark · Describes correct translation
B2 (c) · 1 mark · States x = 2 as axis of symmetry
Worked solution
Set y = 0: x^2 − 4x + 3 = 0 ⇒ x^2 − 4x + 3 = (x−3)(x−1) ⇒ x = 3 or x = 1 so roots are (3,0) and (1,0)
Graph moves 2 units right.
Axis of symmetry is x = 2 (halfway between roots 1 and 3, or using formula).