Hi

the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  and  x = h  is the Line of Symmetry

Y= -4x^2-12x-3   |completing Square of ax^2 + bx + c

y = -4(x - (-3/2))^2 + 9 - 3  |Note: -3/2 = -b/2a

 V(-3/2, 6), a=-4<0. Opens Downward, axis of symmetry x = -3/2

y = -4(x+3/2)^2 +6 

0 = -4(x+3/2)^2 +6

4(x+3/2)^2 = 6

(x+3/2)^2 = 6/4

x = -3/2 ± √6 / 2  roots

domain All real Numbers

range [6,−∞) 



 

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