# Algebra graphing question

#### Manu Baber

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
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
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

#### skipjack

Forum Staff
... horizontal stretch; y-values 1/4 of their original value
That's a vertical "stretch" by factor of 1/4.