Question 941392
 start with:

{{{y = x^2 }}}

{{{ graph( 600, 600, -10, 10, -10, 10, x^2) }}}


now,  multiply coefficient of {{{x^2 }}} by {{{-2}}}

{{{y = -2x^2 }}}

{{{ graph( 600, 600, -10, 10, -10, 10, -2x^2) }}}

{{{f(x)}}} flipped upside down ("reflected about the x-axis") and the parabola for {{{-2x^2 }}} grows twice as fast as {{{x^2}}}, so its graph is  "squeezed"

now add {{{1}}} to {{{x}}} and square it

{{{y = -2(x + 1)^2 }}}


{{{ graph( 600, 600, -10, 10, -10, 10, -2(x+1)^2) }}}


as you can see entire graph is moved one unit to the left


now  add {{{1}}} to {{{y = -2(x + 1)^2 }}}

{{{y = -2(x + 1)^2 +1}}}


{{{ graph( 600, 600, -10, 10, -10, 10, -2(x+1)^2+1) }}}

as you can see entire graph is moved one unit up


so, in short the parent function graph was:
1. flipped upside down ("reflected about the x-axis")  and squized
2. moved one unit to the left
3. moved one unit up