1. Explain how to determine the equation of the function with the following zeros. Be sure to explain each step as you show
how to determine the equation.
-5 multiplicity 2
-2 multiplicity 1

Step-by-step explanation:

Roots of a polynomial

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

Where a is an arbitrary constant.

We are given the following roots:

-5 multiplicity 2 (-5 twice)

-2 multiplicity 1

Thus, the polynomial is:

We are not given any clue about the value of a, so we choose a=1. Multiplying:

Simplifying:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.