Question 1210580


{{{g(x)  = f(x) + C}}}

if {{{C > 0}}} moves it up
if {{{C < 0}}} moves it down

in your case {{{C=0}}}, so {{{g(x)}}}  passes through origin and does not move


{{{y = Cf(x)}}}

if {{{C > 1}}} stretches it in the y-direction
if {{{0 < C < 1}}} compresses it
in your case {{{C=-0.5}}} or {{{-1/2}}}, so {{{g(x)}}}  compresses {{{2}}} times in {{{y}}}-direction

since {{{C=-0.5}}}, {{{g(x)}}} will be flipped upside down :


{{{g(x) = -0.5x^2}}}


since {{{g(x) = -f(x)}}} reflects it about x-axis


so, {{{g(x) }}}compressed {{{2}}} times in {{{y}}}-direction ,  flipped upside down, and reflected about x-axis


{{{ graph( 600, 600, -10, 10, -10, 10, -0.5x^2, x^2) }}}