linear function equation?

Equation of the curve: y = mx²

(x₁, y₁), (x₂, y₂) and (x₃, y₃) are the point lying on the curve.

Hence, (4, a), (12, 18) and (b, 72) lie on the curve.

(12, 18) lies on the curve. Put x = 12 and y = 18 into the equation y = mx²:

18 = m(12)²

18 = 144m

m = 18/144

m = 1/8

Equation of the curve: y = x²/8

(4, a) lies on the curve. Put x = 4 and y = a into the equation y = x²/8:

a = 4²/8

a = 2

(b, 72) lies on the curve. Put x = b and y = 72 into the equation y = x²/8:

72 = b²/8

b² = 576

b = ±√576

b = ±24

The correct way of writing your problem is --

Evaluate a  and  b if --

y = m x^2

Given that when -

x = 4 , y = a ........... (1)

x = 12, y  =  18........(2)

x = b , y  =  72.........(3)

Substitute these values in the given equation  y  =  m x^2  one by one .

from (1) 

=> a  =  m (4)^2   =>   a  =  16 m .......   (A)

from (2)    18  =  m (12)^2   =>   m  =  (18/144)  =  (1/8)

m  =  (1/8)  ............. ( B)

From (1) and (2)  a  = 16/8  =  2  .................. Answer

Again, from (3) 

72  =  (1/8) (b)^2

=>  b^2  =  72*8  =>   b = 24   Answer