Scalings and translations in graphs

[Bugsy23]

Homework Statement

Explain how the parabola that is the graph of f can be obtained from the graph of y=x²

Homework Equations

f(x)=-1/3(x-2)²+3

The Attempt at a Solution

a y-scaling with factor -1/3
a horizontal translation by 2 units to the right
a vertical translation by 3 units upwards

Can someone tell me if that's right or not? Thanks

 

[Mark44]

Looks fine except that I would describe the transformation as a y scaling by a factor of 1/3 and a reflection across the x-axis.

You can check your work by sketching the graph as you have described it, and then verifying that the points on the graph match the formula you have. For example, a few points on the untransformed graph (y = x^2) are (0, 0), (1, 1), and (2, 4). If these points are compressed, reflected, and translated, where do they end up? Do they agree with the formula?

 

[eumyang]

Homework Statement

Explain how the parabola that is the graph of f can be obtained from the graph of y=x²

Homework Equations

f(x)=-1/3(x-2)²+3

The Attempt at a Solution

a y-scaling with factor -1/3
a horizontal translation by 2 units to the right
a vertical translation by 3 units upwards

Can someone tell me if that's right or not? Thanks

If you mean that "y-scaling" = vertical stretch/shrink, then I would consider the first part as incorrect. The way I've learned it, you can only have a vertical stretch/shrink by a positive number factor (ie. "vertical stretch by a factor of 4," "vertical shrink by a factor of 1/2"). The negative in front of the 1/3 indicates another transformation. What is it?

EDIT: Beaten to it. ;) See above post.