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October 11th, 2016, 04:19 AM  #1 
Newbie Joined: Apr 2016 From: Sydney Posts: 5 Thanks: 0  Algebra graphing question
Hi, would any of you know how to solve this question with some algebra as part of the solution? Determine and describe the changes that need to be applied to the graph of y= x^2 to produce the graph of y= 0.25x^2+ 2x+ 0 I'm also not quite sure what this question means by what changes need to be applied? Thanks 
October 11th, 2016, 06:07 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,445 Thanks: 1312 
You could start by applying magnification by a factor of 4 and reflection in the xaxis to get the graph of y = 4(x/4)$^2$ = 0.25x$^2$, and then apply an appropriate translation. 
October 11th, 2016, 06:11 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,569 Thanks: 1272 
get the quadratic function in vertex form by completing the square ... $y = \dfrac{1}{4}x^2  2x$ $y = \dfrac{1}{4}(x^2 + 8x)$ $y = \dfrac{1}{4}(x^2 + 8x + 16) + 4$ $y = \dfrac{1}{4}(x+4)^2 + 4$ transformations to the parent graph, $y=x^2$ ... (1) $y=(x+4)^2$ ... horizontal shift left 4 units (2) $y=\dfrac{1}{4}(x+4)^2$ ... horizontal stretch; yvalues 1/4 of their original value (3) $y=\dfrac{1}{4}(x+4)^2$ ... reflection over the xaxis (4) $y=\dfrac{1}{4}(x+4)^2+4$ ... vertical shift up 4 units 
October 11th, 2016, 08:54 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,445 Thanks: 1312  
October 11th, 2016, 10:52 AM  #5  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
Source: http://cms.cerritos.edu/uploads/pmat...formations.pdf . Last edited by Math Message Board tutor; October 11th, 2016 at 10:56 AM.  

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