Question

The graph of y=x^2-2x+1 is translated by the vector (2 3).The graph so obtained is reflected in the x-axis and finally it is stretched by a factor 2 parallel to y-axis.Find the equation of the final graph is the form y=ax^2+bx+c, where a,b and c are constants to be found.

Answer 1

y = (x-1)^2
To move right 2 and up 3, you get a new
y = ((x-2)-1)^2 + 3 = (x-3)^2 + 3
reflection gives you y = -((x-3)^2 + 3)
stretching gives you y = -2((x-3)^2+3)