Answer:
x^2 +6x +8
Step-by-step explanation:
The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).
The standard form of the function with zeros p and q is ...
(x -p)(x -q) = x^2 -(p+q)x +pq
So, for zeros p=-4, q=-2, the standard form is ...
x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8
We can check to make sure the above vertex point satisfies this function:
(-3)^2 +6(-3) +8 = 9 -18 +8 = -1
The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.
The function is ...
y = x^2 +6x +8
