Unit 5
3 marks · EasyThe curve y = x^2 - 9 cuts the x-axis at two points.
Solve the equation x^2 - 9 = 0 to find the x-coordinates where the curve cuts the x-axis.
On the grid below, sketch the graph and indicate the points where it crosses the x-axis.
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.
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(a) x = 3, x = -3
(b) — · must show parabola with vertex below x-axis, crosses x-axis at x = 3 and x = -3
Must show: roots at x = 3, x = -3, parabola passes through (0, -9)
Common mistakes: Omitting negatives; Mistaking y-intercept for x-intercept
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets x^2 - 9 = 0 and factors or solves for x.
A1 (a) · 1 mark · Gives both solutions: x = 3 and x = -3.
B1 (b) · 1 mark · Correct sketch with labelled intercepts at x = -3 and x = 3.
Worked solution
a) x^2 - 9 = 0 \implies x^2 = 9 \implies x = 3 or x = -3.
b) The graph is a parabola opening upwards, passing through (0, -9). It crosses the x-axis at (3, 0) and (-3, 0).