Question

How to find the quadratic function given the vertex (2,-4) and the point (1,-1)?

Answer 1

Since the vertex is at `(2, -4)` we can deduce

`f(x) = a(x-2)^2-4`

for some constant `a`

Then from the point `(1, -1)` we get:

`-1 = f(1) = a(1-2)^2-4 = a-4`

Add `4` to both ends to get

`a = 3`

So:

`f(x) = 3(x-2)^2-4 = 3x^2-12x+8`