Jillian claims that the graph of the function y = (-x)2 is the same as the graph of the function y = -(x2). Is she correct? Explain your reasoning.

Question

Which is the correct letter?

 

A. No; squaring a negative number yields a positive number, while taking the opposite of a squared number yields a negative number
B. No; one is a function and the other is not

C. Yes; they are both parabolas

D. Yes; (−x)2 = −x2 = −(x2)

 

Answer 1

Lets compare the two.

 

y = (-x)² = (-x)(-x) = x²

 

y = -(x²) = -x²

 

 

One is a parabola that opens upward, whereas the other is a parabola that opens downward.