Which function belongs to which parabola?

I know that the x^2 ones are parabolas opening down, but how do you distinguish them?

f(x) = x^2 - 2

g(x) = -(x - 2)^2

h(x) = x^2 -2x

j(x) = -x^2 + 2x

Guest Nov 20, 2018

#1**+1 **

f(x) = x^2 - 2

This is the parent graph y = x^2 just shifted down 2 units

So....A

(x) = - ( x - 2)^2

This is the parent graph "flipped" over the x axis and shited to the right by 2 units

So...C

f(x) = x^2 - 2x

This turns upward.......it's easier to see if we write it this way

f(x) = x ( x - 2)

This has "zeros" at x = 0 and x = 2

So....it turns upward and crosses the x axis at x = 0 and x = 2

So...B

f(x) = -x^2 + 2x

If we write this as f(x) = - (x^2 - 2x).....it's the same graph as B "flipped over" the x axis

So.....D

Hope that helps !!!

CPhill
Nov 20, 2018