Question 669615
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Hi,
 standard forms are a 'need to know'
the vertex form of a Parabola opening up(a>0) or down(a<0)is: {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry Pt(2,-5) on the curve
y=-2x^2+3  V(0,3), -2< 0, opening downward, Line of Symmetry is x = 0 (y=axis)
function(satisfies the vertical Line test) describes a parabola. 
domain:  (&#8722;&#8734;,&#8734;)
range:   (&#8722;&#8734;,3]
Transformation(shifted three units upward and four units to the left) y = -2(x+4)^2 + 6 
{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(-4,6,-4,-6))  , grid(1),
circle(0, 3,0.3),
circle(2, -5,0.3),
graph( 300, 300, -6, 6, -6, 6,0,-2x^2+3,-2(x+4)^2 + 6 
))}}}