How can completing the square help with graphing transformations?

[shoook]

1. Graph the function f(x)=x^2+4x+3 by starting with the graph of y=x^2 and using transformations.



2.



3. I know the graph opens up, but I don't understand transformations or how to solve them, any help would be greatly appreciated.

 

[bel]

For any function f(x), f(x-a) moves the graph right by a units, a*f(x) stretches the graph by a factor of "a", f(ax) increases the frequency of the graph "a" times, f(x)-a moves a graph down by "a" units.

 

[rock.freak667]

Well to help you see better change f(x) into the completed square form

 

[robphy]

If you think physically (i.e. like a freefall problem), you can almost immediately pick out the meaning of the constant 3 term and the 4x term... then transform the original y=x^2 appropriately.

 

[HallsofIvy]

To repeat the very good advice of rock_freak667, complete the square- and it all shall be made clear to you!