Graphs 4

4 marks · Normal

For the quadratic graph :

(a)

Find the x-coordinates where the curve meets the x-axis.

[2 marks]

(b)

State the coordinates of the turning point.

[2 marks]

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(a) x = 1 and x = 3

(b) (2, -1)

Common mistakes: Wrong formula application; Arithmetic errors

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Forms and solves x^2 - 4x + 3 = 0 for x.

A1 (a) · 1 mark · Gives both correct x-values: 1 and 3.

M2 (b) · 1 mark · Uses formula for vertex: x = -b/2a, finds y.

A2 (b) · 1 mark · States correct turning point coordinates: (2, -1).

Worked solution

(a) Solve x^2 - 4x + 3 = 0:

So x = 1 and x = 3.

(b) The turning point is at x = -b/2a = 4/2 = 2, y = (2)^2 - 4*2 + 3 = 4 - 8 + 3 = -1. So (2, -1).