Write the equation in factored form, of a parabola that has a vertex of (1,-16) and passes through the point (3, -12)

Step-by-step explanation:

f(x) = a(x-h)²+k  - vertex form with vertex (h, k)

So with vertex (1, -16) the vertex form is:

f(x) = a(x - 1)² - 16

The parbola passing through the point (3, -12) means that if x=3 then f(x)=-12

-12 = a(3 - 1)² - 16

-12 +16 = a·2² -16 +16

    4 = 4a

   a = 1

Our equation in vertex form is:   f(x) = (x - 1)² - 16

Factored form of equation of parabol is f(x) = a(x-x₁)(x-x₂) where x₁, x₂ are zeros of the parabola

So to write factored form we need zeros:

(x - 1)² - 16 = 0

(x - 1)² = 16

x - 1 = 4      or   x - 1 = -4

x₁ = 5                 x₂ = -3

So a=1 and the factors are:  (x-5) and (x+3)

Therefore the equation in factored form is:

            f(x) = (x + 3)(x - 5)

step-by-step explanation: