Question

Make y the subject of the formula

k= y^2 + a

Answer 1

y =
`√((k-a))`

Explanation:

k= y^2 + a

k-a= y^2

y^2 = k-a

y = (k-a)^(1/2)

y =
`√((k-a))`

Answer 2

`\displaystyle{y=\pm √(k-a)}`

Explanation:

To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².

`\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}`

Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)

Then square root both sides to get rid of the exponents of y-term:

`\displaystyle{√(k-a)=√(y^2)}`

If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:

`\displaystyle{\pm √(k-a)=y}`

Therefore, the new equation written in term of y is:

`\displaystyle{y=\pm √(k-a)}`