9. y=-1/4x^2+4x-19 group y=(-1/4x^2+4x)-19 undistribute -1/4 y=-1/4(x^2-16x)-19 take 1/2 of -16 and squer it to get 64 then add neg and pos inside y=-1/4(x^2-16x+64-64)-19 factorperfect square y=-1/4((x-8)^2-64)-19 expand y=-1/4(x-8)^2+16-19 y=-1/4(x-8)^2-3 vertex is (8,-3)
10. group y=(1/4x^2-3x)+18 undistribute y=1/4(x^2-12x)+18 take 1/2 of -12 and square it and add neg and pos isndie y=1/4(x^2-12x+36-36)+18 factor y=1/4((x-6)^2-36)+18 expand y=1/4(x-6)^2-9+18 y=1/4(x-6)^2+9 get to form (x-h)^2=4p(y-k) minus 9 both sides and times 4 (x-6)^2=4(y-9) (x-6)^2=4(1)(y-9) so 1>0 so opens up and focus is 1 above vertex vertex is (6,9) so focus i (6,10)
11. y=(-1/6x^2+7x)-80 y=(-1/6)(x^2-42x)-80 take 1/2 of linear coefient and squer it and add negative and positive inside -42/2=-21, (-21)^2=441 y=(-1/6)(x^2-42+441-441)-80 factor perfect square the square y=(-1/6)((x-21)^2-411)-80 expand y=(-1/6)(x-21)^2+73.5-80 y=(-1/6)(x-21)^2-6.5 add 6.5 to both sid y+6.5=(-1/6)(x-21)^2 times both sides by -6 -6(y+6.5)=(x-21)^2 (x-21)^2=-6(y+6.5) (y-21)^2=4(-3/2)(y-(-6.5)) vertex is -3/2<0 so directix is above it is -3/2 or 1.5 units above the vertex up is y so -6.5+1.5=-5 the directix is y=-5
11. in form (y-1)^2=4p(x+3) opens left or right (y-1)^2=4(4)(x+3) vertex is (-3,1) 4>0 so opens right dirextix is to left it is 4 units to left (-3,1) left right is x 4 left of -3 is -4-3=7 x=-7 is da directix
