Question

Which of the following describes the translation of the graph of y = x 2 to obtain the graph of y = -x 2 - 3?

Answer 1

Im assuming that x 2 means x^2 ( x squared)

y = -x^2 is the reflection of y = x^2 in the x axis

Then the - 3 moves the graph down 3 units

so the transformation is described by

a reflection in the y axis , then a translation 3 units downwards

Answer 2

It describes a reflection in the x axis and then a translation of 3 units down of the entire graph.

Explanation:

When you multiply an expression by a constant term your expanding the values by that constant term. When the sign is negative your making a relfection among the x axis of all the poinos the graph so - x^2 is only the original graph reflected in the x axis.

When you add/subtract a constant number to the whole expression of x , you move up/down the graph by that number of units, You are subtracting 3 so the new graph is the transalation of all points by 3 units down of the reflected orginal graph.