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October 11th, 2016, 04:19 AM   #1
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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?

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October 11th, 2016, 06:07 AM   #2
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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.
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October 11th, 2016, 06:11 AM   #3
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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
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October 11th, 2016, 08:54 AM   #4
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Quote:
Originally Posted by skeeter View Post
... horizontal stretch; y-values 1/4 of their original value
That's a vertical "stretch" by factor of 1/4.
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October 11th, 2016, 10:52 AM   #5
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Quote:
Originally Posted by skeeter View Post

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


Source:
http://cms.cerritos.edu/uploads/pmat...formations.pdf


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