Question

What are `a` and `k` so the points `(1,15)` and `( 2,- 5)` are on the graph `y = a ( x + 1) ^ { 2} + k`?

Answer 1

`a =-4` and `k = 31`.

Explanation:

We write a system of equation

`15 = a(1 + 1)^2 + k`

`15 = 4a + k`

Now

`-5 = a(2 + 1)^2 + k`

`-5 = a(9) + k`

`-5 = 9a + k`

So if we substitute the second equation into the first

`15 = 4a + (-5 - 9a)`

`15 = 4a - 5 - 9a`

`20 = -5a`

`a = -4`

Now solve for `k`.

`15 = 4(-4) + k`

`15 + 16 = k`

`k = 31`

Hopefully this helps!