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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Answered by Shavon D. Maths tutor

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Line AB has equation 4x+5y+2=0. If the point P=(p, p+5) lies on AB, find P . The point A has coordinates (1, 2). The point C(5, k) is such that AC is perpendicular to AB. Find the value of k.


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