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

Jun 20, 2018

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

#### Explanation:

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

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