Question 1192297
The standard form of a quadratic function presents the function in the form

{{{f(x)=a(x-h)^2+k}}}

the basic parabola graph of  f(x)=x^2  is horizontally shifted left (h < 0) and right (h > 0) 
vertically shifted   up  (k > 0)  or shift it down  (k < 0) .

1. The graph of {{{y=-(1/2)x^2}}} shifted {{{3}}} units to the right and {{{3}}} units upward.

if shifted {{{3}}} units to the right =>{{{h=3}}}
if shifted {{{3}}} units upward=>{{{k=3}}}
{{{y=-(1/2)(x-3)^2+3}}}


{{{ graph( 600, 600, -15, 15, -15, 15, -(1/2)x^2, -(1/2)(x-3)^2+3) }}} 


2. the graph of {{{y=-4x^2}}} shifted {{{8 }}}units to the left and {{{4 }}}units downward.
{{{8}}} units to the left =>{{{h=-8}}}
 {{{4}}} units downward=>{{{k=-4}}}
{{{y=-4(x-(-8))^2-4}}}
{{{y=-4(x+8)^2-4}}}


{{{ graph( 600, 600, -15, 15, -15, 15, -4x^2, -4(x+8)^2-4) }}} 


3. the graph of {{{y=(3/4)x^2 shifted {{{2 }}}units to the left and {{{2}}} units downward.

{{{2}}} units to the left =>{{{h=-2}}}
 {{{2}}} units downward=>{{{k=-2}}}

{{{y=(3/4)(x+2)^2-2}}}


{{{ graph( 600, 600, -15, 15, -15, 15, (3/4)x^2, (3/4)(x+2)^2-2) }}}