How is the graph of #h(x)=-7-x^2# related to the graph of #f(x)=x^2#?

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Answer 1 · 2017-10-27T21:18:03

Rotates the graph by 180 degrees bout its vertex and then lowers it by 7.

#-x^2# shape is #nn# whilst #x^2# is #uu#

The vertex for each being in the same place of #(x,y)->(0,0)#

The #-7# of #-7-x^2# lowers the graph of #-x^2# by 7

Example Consider #y=-x^2#

Set #x_1# as 2

Then #y_1=-(2^2)=-4# Call this point 1

#color(green)(P_1->(x_1,y_1)=(2,-4))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vertically lower this point by 7 and call the new point #P_2#

So just considering the coordinates we have:

#color(blue)(P_2->(x_1,color(white)("d")y_1-7)=(2,-4-7)=(2,-11))#

...................................................................................................
Compare to #y_2=(x_2)^2-7#

Set #x_2=x_1# then we have:

#color(blue)(y_2=-(x_1)^2-7 => -2^2-7 = -11 ->P_2)#

Tony B