Describe the set of transformations that will transformthe curve y=x^ to the curve y=x^2 + 4x - 1
First complete the square on the curve in the answer to obtain y=(x+2)2 - 5 Now if you were to call your original equation y=f(x) you could see that the new equation is simply y=f(x+2) - 5This is now just a case of remembering the rules of transformationsThe bit inside the brackets provides a translation through the vector (-2 0) and the bit outside the brackets provides a translation through the vector (0 -5) Putting these two vectors together gives a translation through the vector (-2 -5) which is a translation 2 units in the negative x direction and 2 units in the negative y direction
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