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Isobel from Wycombe High School has first identified the given equations as L and K, and then obtained I and J by reflecting these two in the x-axis, and finally obtained the remaining equations by translating I,J,K,L to the left by 6 for E,F,G,H and by 12 for B,A,C,D. This gives the following expressions:
A: $y=-(-(x+12)^2+12(x+12)-36)$
B: $y=-((x+12)^2-12(x+12)+27)$
C: $y=-(x+12)^2+12(x+12)-36$
D: $y=(x+12)^2-12(x+12)+27$
E: $y=-((x+6)^2-12(x+6)+27)$
F: $y=-(-(x+6)^2+12(x+6)-36)$
G: $y=-(x+6)^2+12(x+6)-36$
H: $y=(x+6)^2-12(x+6)+27$
I: $y=-(x^2-12x+27)$
J: $y=-(-x^2+12x-36)$
K: $y=-x^2+12x-36$
L: $y=x^2-12x+27$
When expanded out this gives the simplified equations for the parabolas as:
A: $y=x^2+12x+36$
B: $y=-x^2-12x-27$
C: $y=-x^2-12x-36$
D: $y=x^2+12x+27$
E: $y=-x^2+9$
F: $y=x^2$
G: $y=-x^2$
H: $y=x^2-9$
I: $y=-x^2+12x-27$
J: $y=x^2-12x+36$
K: $y=-x^2+12x-36$
L: $y=x^2-12x+27$
(Another way of getting B,A,C,D is by reflecting I,J,K,L in the y-axis instead of translating to the left by 12)
Which Parabola?
Age 16 to 18
Challenge Level 
Isobel from Wycombe High School has first identified the given equations as L and K, and then obtained I and J by reflecting these two in the x-axis, and finally obtained the remaining equations by translating I,J,K,L to the left by 6 for E,F,G,H and by 12 for B,A,C,D. This gives the following expressions:
A: $y=-(-(x+12)^2+12(x+12)-36)$
B: $y=-((x+12)^2-12(x+12)+27)$
C: $y=-(x+12)^2+12(x+12)-36$
D: $y=(x+12)^2-12(x+12)+27$
E: $y=-((x+6)^2-12(x+6)+27)$
F: $y=-(-(x+6)^2+12(x+6)-36)$
G: $y=-(x+6)^2+12(x+6)-36$
H: $y=(x+6)^2-12(x+6)+27$
I: $y=-(x^2-12x+27)$
J: $y=-(-x^2+12x-36)$
K: $y=-x^2+12x-36$
L: $y=x^2-12x+27$
When expanded out this gives the simplified equations for the parabolas as:
A: $y=x^2+12x+36$
B: $y=-x^2-12x-27$
C: $y=-x^2-12x-36$
D: $y=x^2+12x+27$
E: $y=-x^2+9$
F: $y=x^2$
G: $y=-x^2$
H: $y=x^2-9$
I: $y=-x^2+12x-27$
J: $y=x^2-12x+36$
K: $y=-x^2+12x-36$
L: $y=x^2-12x+27$
(Another way of getting B,A,C,D is by reflecting I,J,K,L in the y-axis instead of translating to the left by 12)
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