Answer:
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)
