posted by -Untamed- .
Analyzing Quadratic Functions
describe how the graphs of the following functions relate to the graph of y=x^2.
Could someone please tell me what that means? I sort of understand it, but I want to get it perfectly straight.
y = (x+5)^2
Since it's in the brackets, that would mean go five units horizontally. And would it go negative because doesn't it go in the opposite direction?:S
y = x^2-7. Is -7 the slope?
y = 5+(x-2)^2. This one is confusing.
You are correct on the first one. The new function is x^2 if we use a value 5 less than originally. That is, the graph is shifted 5 units to the left.
y = x^2 - 7
is just the graph of y=x^2, but shifted down 7 units.
Now you come upon shifting in both directions.
shift 2 units right, then 5 units up.
In general, the graph of y = f(x) is shifted h units to the right and k units up if
(y-k) = f(x-h)
You can see that the new function is just f(x) if we adjust the values of x and y by h and k, respectively.
If you want to play around with graphs, go to
rechneronline dot de slash function-graphs
You can type in a function f(x) of your choosing (they start out showing x^2). Then, just substitute (x-2) for x and see how the graph shifts.
It's also cool because you can show both graphs at once, in different colors.