If f(x) = 2x3 + 18x2 + 56x + 40 and f(-1) = 0, then find all of the zeros of
f(x) algebraically.

Step-by-step explanation:

Part A:

From the given graph it is clear that the coordinates of ABCD are A(-4,4), B(-2,2), C(-2,-1) and D(-4,1).

The vertices of A'B'C'D' are A'(4,1), B'(2,-1), C'(2,-4) and D'(4,-2).

If the graph of ABCD is reflected across the y-axis, then

(x,y)⇆ (-x,y)

Using this rule the vertices of ABCD after reflection across the y-axis are A₁(4,4), B₁(2,2), C₁(2,-1), and D₁(4,1).

If the graph of A₁B₁C₁D₁ is translated 3 units down, then

(x,y)⇆ (x,y-3)

The vertices of ABCD after reflection across the y-axis and translation 3 units down.

A_1(4,4)⇆A'(4,1)

B_2(2,2) ⇆B'(2,-1)

C_1(2,-1) ⇆C'(2,-4)

D_1(4,1)⇆ D'(4,-2)

Therefore the graph of ABCD is reflected across the y-axis and translates 3 units down.

Part B:

Reflection and translation is a rigid transformation. It means the size and shape of the figure remain the same.

Therefore the figures ABCD and A'B'C'D' are congruent.