definitions

A function is symmetric about the x-axis if and only if replacing y with -y will yield the same function (explain why)

A function is symmetric about the y-axis if and only if replacing x with -x will yield the same function (explain why)

A function is symmetric about the origin if and only if it is both symmetric about the x and y axis

x-intercepts are points which lie on the line y = 0. find where y= 16-x^2 and y = 0 intersect

y-intercepts are points which lie onthe line x = 0. find where y = 16-x^2 and x = 0 intersect

2. You can re-write the equation by rearranging and grouping terms, and then completing the square for both x and y

x^2 + 5x + y^2 - 2y + 6 = x^2 + 5x + (5/2)^2 -(5/2)^2 + y^2 - 2y + 1 - 1 + 6 = (x+(5/2))^2 + (y+1)^2 + -(5/4) = 0

Hence the equation can be re-written as (x+(5/2))^2 + (y+1)^2 = (5/4) In this form, can you tell me what the center and radius is? If you have a problem with completing the square let me know.

3.

To be parallel with a line means having the same slope. calculate the slope of the line through the points (1,1) and (-1,5) using (rise over run)

Using m and the point (7,3) plug them into the point slope form which is just rewriting the above slope formula to get the equation for your desired line.