A 3 x2+ 12 x + 25 = 3 [ x2 + 4x ] + 25 = 3 [ (x)2 +2 (x) (2) + (2)2 - (2)2] + 25, for completing square (2)2 - (2)2 are added , a2 + 2ab + b2 = (a + b)2 , here a = x , b = 2 = 3[ (x +2)2 -4]+25 = 3 (x+2)2 - 12 + 25 = 3 (x +1)2 + 13 3x2+ 12 x + 25 = 3 (x +2)2 + 13 , a=3 , h = 2 , k = 13 y = 3x2 + 12 x + 25 = 3 (x +2)2 + 13 for y- intercept , x = 0 y = 3* 02 + 12 '0 + 25 = 0 +0 + 25 = 25, ory = 3 (0+2)2 + 13 = 3* 4 + 13 = 12 + 13 = 25, y- intercept ( 0 , 25 ) y = 3(x+2)2 + 13 , a =3 ,h =2 , k = 13 . a = 3 is positive , minimum point is ( - h, k ) minimum point ( -2 , 13 ) These are shown in attached graph y = 3 x 2 + 12 x + 25 40 30 y-intercept : ( 0 , 25 ) 20 minimum point : ( -2 , 13 )10 -20 -10 0 10 20 30