Processing Math: Done

From Förberedande kurs i matematik 1

To determine all the points on the curve y=3x2−12x+9 which also lie on the x-axis we substitute the equation of the x-axis i.e. y=0 in the equation of the curve and obtain that x must satisfy

0=3x2−12x+9.

After dividing by 3 and completing the square the right-hand side is

x2−4x+3=(x−2)2−22+3=(x−2)2−1

and thus the equation has solutions x=21 i.e. x=2−1=1 and x=2+1=3.

The points where the curve cut the x-axis are (1,0) and (3,0).