Algebra graphing question

Apr 2016
5
0
Sydney
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
 

skipjack

Forum Staff
Dec 2006
21,478
2,470
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.
 

skeeter

Math Team
Jul 2011
3,355
1,848
Texas
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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