Algebra Transformations

Question

Describe the transformations in the equation y= -4(x-3)^2+7

Answer 1

The basic equation is y = x². The transformed equation is y = -4(x-3)² + 7

1. The -4 is a vertical dilation (stretch) by a factor of 4. The negative sign reflects the graph across the x-axis.
2. The -3 is a horizontal translation (shift) right 3 units
3. The +7 is a vertical translation (shift) up 7 units

Answer 2

This equation represents a parabola. Because of the negative sign, it has a maximum value at its vertex. There are two transformations:

1) The x-3 part of the equation shifts the parabola maximum right by 3 so that the vertex is at x=3.

2) The +7 part of the equation shifts the parabola up by 7, so that the vertex occurs at y=7.

Note that the squaring ox x-3 is NOT a translation. It defines the shape of the curve as a parabola. Likewise, the multiplier of 4 is NOT a translation. It defines the width of the parabola. If it was a larger number, the parabola would be narrower; a smaller number would widen the parabola.