The equation of parabola parallel to y-axis is y=Ax2+Bx+C . . . (i) The point (0,4),(1,9) and (4,5) lies on Eq. (i). Then, ‌‌4=0+0+C⇒C=4 . . . (ii) ‌9=A+B+C‌ ‌ or ‌‌9=A+B+4‌(∵C=4) ‌A+B=5‌‌‌...‌ (iii) ‌ ‌ and ‌‌5=16A+4B+C‌‌(∵C=4) ‌ or ‌‌5=16A+4B+4‌ ∴‌16A+4B=1‌ or 4A+B=‌
1
4
. . . (iv) Solving Eqs. (iii) and (iv), we get ‌‌A=‌
−19
12
,B=‌
79
12
. . . (v) Substituting the values of A,B and C from Eqs. (ii) and (v) in Eq. (i), then equation of parabola is y=‌