My Math Forum Algebra graphing question

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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: 16,591 Thanks: 1199 You could start by applying magnification by a factor of 4 and reflection in the x-axis 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: 2,293
Thanks: 1126

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; y-values 1/4 of their original value

(3) $y=-\dfrac{1}{4}(x+4)^2$ ... reflection over the x-axis

(4) $y=-\dfrac{1}{4}(x+4)^2+4$ ... vertical shift up 4 units
Attached Images

October 11th, 2016, 08:54 AM   #4
Global Moderator

Joined: Dec 2006

Posts: 16,591
Thanks: 1199

Quote:
 Originally Posted by skeeter ... horizontal stretch; y-values 1/4 of their original value
That's a vertical "stretch" by factor of 1/4.

October 11th, 2016, 10:52 AM   #5
Banned Camp

Joined: Jun 2014
From: Earth

Posts: 945
Thanks: 191

Quote:
 Originally Posted by skeeter (2) $y=\dfrac{1}{4}(x+4)^2$ ... horizontal stretch; y-values 1/4 of their original value
Quote:
 Originally Posted by skipjack That's a vertical "stretch" by factor of 1/4.
It's called a "vertical compression by a factor of 1/4."

Source:

.

Last edited by Math Message Board tutor; October 11th, 2016 at 10:56 AM.

 Tags algebra, graphing, question

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Nmbvc0 Calculus 0 April 2nd, 2013 10:36 PM robotle18 Academic Guidance 0 February 23rd, 2012 06:26 PM lordj0hn Applied Math 0 July 11th, 2010 12:55 PM you_of_eh Algebra 12 September 29th, 2009 11:16 AM

 Contact - Home - Forums - Top