Question

The curve with equation =2is transformed to the curve with equation 2+6+5. Describe fully the transformations involved.

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Answer 1

I assume you mean the transformation of y=x² to y=x²+6x+5?

x²+6x+5 can be written x²+6x+9-4=(x+3)²-4.

So y=x² is transformed to y=(x+3)²-4.

The vertex of the parabola y=x² is at the origin (0,0).

The vertex of the parabola y=(x+3)²-4 is at (-3,-4).

So the transformation is to move the vertex from the origin 3 units to the left and 4 units down.