SOLUTION: Sketch the function f defined y = x^2 for -2 < x < 2 use this graph to sketch the following transformation of f. a) y = x^2-4 b) y = -x^2 c) y = 5x^2 can you please expla

We start with this basic squaring function which is 

y = x²



Now the graph of 

(a)  y = x² - 4  

looks exactly like the graph of y = x² except that the - 4
added on the right shifts the graph down 4 units, and makes
the graph drawn in green below:



Now the graph of 

b)  y = -x²   

also looks exactly like the graph of y = x² except that multiplying
the right side by -1 reflects the graph across the x-axis (as if the
x-axis were a mirror; the reflection would be the graph drawn in green 
below:



---

d)  y = 5x²   

This one is not going to look exactly like the graph of y = x² 
because multiplying the right side by 5, which is a number greater
than 1, is going to stretch the graph vertically.  It is the same
as if the graph of y=x² had been drawn on a rubber sheet and the 
rubber sheet stretched 5 times its height.  This stretched graph
would be the graph drawn in green below:



Edwin