shape of y= x^3 but reflected over the x axis and shifted two units to the left

Answer 1

y = x^3

reflected over the x axis means replace y by -y (every point (x,y) is replaced by (x,-y))

-y = x^3

y =-x^3

shift 2 units left means replace x by x+2, point (0,0) shifts left to become (-2,0) -2+2=0

y = -(x+2)^3

or expand to get

y =-(x^3 + 6x^2 + 12x + 8)

y = -x^3 -6x^2 -12x - 8