What the equation of the quadratic function in standard form represented by the graph

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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.