Question

How can I solve `y=a(x-1)^2+k` when they only give me two points which are : (2,6) and (3,12)?

Answer 1

You just need to plug the points and then solve that.

Explanation:

Because `(2,6)` is in the function, we can plug `6` as `y` and `2` as x.
From that we get `6=a(2-1)^2+k`
`6=a+k`
Same for the next point: `12=a(3-1)^2+k`
`12=2^2a+k`
`12=4a+k`

Now we have this system of equations to solve:
`a+k=6`
`4a+k=12`
Solving it leads to the conclusion that `a=2,k=4`.