In the diagram, the curve y=9x2−9 cuts the x-axis at two points M and N. Find the coordinates of M and N.

To find the points where the curve y = 9x^2 - 9 cuts the x-axis, we need to set y = 0 and solve for x. This is because the x-axis is defined by y = 0.

So, we have:

0 = 9x^2 - 9

We can simplify this equation by dividing through by 9:

0 = x^2 - 1

This is a difference of squares, which can be factored as follows:

0 = (x - 1)(x + 1)

Setting each factor equal to zero gives the solutions x = 1 and x = -1.

Therefore, the curve y = 9x^2 - 9 cuts the x-axis at the points M(1, 0) and N(-1, 0).