Answer:
y = - (x - 1)²(x + 2)(x + 6)
Step-by-step explanation:
The roots from the graph are
x = - 6 , then factor is (x + 6)
x = - 2 , then factor is (x + 2)
x = 1 ( multiplicity 2 ) , then factor is (x - 1)² then
y = a(x - 1)²(x + 2)(x + 6) ← a is a multiplier
To find a substitute any point on the graph into the equation
Using (0, - 3 ), then
- 3 = a(- 1)²(2)(6) = 12a ( divide both sides by 12 )
- = a
Then
y = - (x - 1)²(x + 2)(x + 6)