I need help understanding how to identify the transformations when the quadratic is in factored form.

Question

f(x) = (x+3)(x-1)

Thanks...

Answer 1

Just looking at the factors will not work, because you can't see the translations.

Expanding and then completing the square,

(x+3)(x-1)
= x^2+2x-3
= (x^2+2x+1)-4
= (x+1)^2 - 4
So, that's x^2, translated left 1 and down 4

Or, using symmetry, you know the axis of symmetry is midway between the roots of -3 and 1, or at x = -1

SO, that means the equation will be

y = (x+1)^2 + k
Now you can expand the original and this one, and find that k = -4.