Question

explain how the graph of each given function is a transformation of the graph y=x^2
b.Y=-2x^2 c.Y=(x-5)^2 d.Y=(-3x)^2

Answer 1

Remember what is meant by a transformation. If you have a fuction, like the one you list, than if you add a constant to it or multiply it by a constant then the graph will look similar in some fashion. It will have an interesting effect on the graph, but it will in some way be the same. This what is called a linear transformation. Some times the input to the function is manipulated. Like instead of x you replce it with x+2 or some other consant or even 2x. The function will then be similar to the original in some basic way. Try graphing y=x^2 anlong with y=-2x^2 on the same plot. What was the change? Do that with each new transformation you are interested in and see what the effect is to y=x^2. The result will be obvious, ie. graph moves to the right, grah is mirrored, graph opens upward faster, etc.