This lesson gives practice with all the graphical transformations:
Before practicing the multistep exercises on this page, you should
practice
singlestep transformations, all mixed up:
jump to the exercises at the bottom, and clickclickclick to check your understanding.
When you're successfully answering all the question types, then you're ready for this current lesson!
Graph $\,y = 3(x2)^2 + 5\,$ by starting with a ‘basic model’ and successively applying graphical transformations.
EQUATION  ACTION  GRAPHICAL RESULT (WORDS) 
GRAPHICAL RESULT (cumulative graph) 
COMMENTS  
$y = x^2$  the ‘basic model’  (the starting graph)  start with the graph of the squaring function  
$y = (x1)^2$  replace every $\,x\,$ by $\,x1\,$  right $\,1\,$ 
when applying a transformation that changes the $\,x\,$values of points, use the phrase ‘replace every $\,x\,$ by ...’ 

$y = 3(x1)^2$  multiply previous $\,y\,$values by $\,3\,$ 
vertical stretch, $\,(a,b) \mapsto (a,3b)\,$ 
when applying a transformation that changes the $\,y\,$values of points, use the language ‘do something to previous $\,y\,$values’; the notation ‘$\,(a,b) \mapsto (a,3b)\,$’ is read as ‘$\,(a,b)\,$ maps to $\,(a,3b)\,$’; it clearly shows that the $\,y\,$values of previous points are getting multiplied by $\,3\,$ 

$y = 3(x1)^2 + 5$  add $\,5\,$ to previous $\,y\,$values  up $\,5\,$ 
Other orders will work.
For example:

Give the equations and actions that produce the successive desired graphical results. Check your answers by clicking the ‘SHOW ANSWER’ buttons. 

EQUATION  ACTION  GRAPHICAL RESULT  
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
