Question

Which of the following best describes the transformations of y=x^2 so that the resulting equation is as follows?

y=(x-6)^2-8

• The graph of the equation is translated 6 units right and 8 units down

• The graph of the equation is translated 6 units left and 8 units down

• The graph of the equation is translated 8 units right and 6 units down

• The graph of the equation is translated 6 units right and 8 units up

• None of these describe the transformations

Answer 1

The equation y=(x-6)^2-8 represents a transformation of y=x^2 where the graph is translated 6 units right and 8 units down.

Step-by-step explanation:

The transformations of the equation y = x^2 to y = (x-6)^2 - 8 involve a horizontal translation and a vertical translation of the graph of the quadratic function.

Specifically, the graph is shifted to the right by 6 units and down by 8 units.

The form of the equation indicates these transformations directly: the horizontal shift is dictated by the expression (x - 6), showing a shift to the right, and the vertical shift is shown by the -8 at the end of the equation, indicating a shift downwards.