The y-intercept will be a constant times the product of the roots. Here, the product of the roots is (-2)(4) = -8, so the constant of interest is -16/-8 = 2. That constant is the coefficient of the leading term of the quadratic, so is a multiplier of the factored form.
y = 2(x +2)(x -4)
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For root p, (x-p) is a factor in the factored form.
