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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

 

 Nov 20, 2018
 #1
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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   !!!

 

 

cool cool cool

 Nov 20, 2018

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