In the table the entries in the two columns have a common si

In the table, the entries in the two columns have a common, simple quadratic relationship, y = ax^2. Find the missing entry.

This is very simple

First find the value of a.

As given at x =1/2 the value of y = 1/2

Put this into given relation y = ax^2

1/2 = a(1/2)^2

1/2= a(1/4)

a = 2

Repeat for second data for confirmation

As given at x =1 the value of y = 2

Put this into given relation y = ax^2

2 = a(1)^2

2= a(1)

a = 2

Repeat for second data for confirmation

As given at x =2 the value of y = 8

Put this into given relation y = ax^2

8 = a(2)^2

8= a(4)

a = 2

So by these calculation it is confirm that the value of a = 2

So our curve is y = 2x^2

Now we have to found x for y =50

y = 2x^2

50 = 2x^2

x^2 = 25

x= 5 or -5