Question

Exercises 12.3 Complete the following: 1. Complete the squares for each quadratic, list the center labeling its translated center: (g) x^2 + y^2 + 4x = 0

Answer 1

EXPLANATION

Considering the equation x^2 + y^2 + 4x = 0

As we already know, the circle equation with a radius r, centered at (a,b) is:

`(x-a)^2+(y-b)^2=r^2`

Rewrite x^2 + y^2 + 4x = 0 in the form of the standard circle equation:

Group x-variables and y-variables together:

`(x^2+4x)+y^2=0`

Convert x to square form:

`(x^2+4x+4)+y^2=4`

Convert to square form:

`(x+2)^2+y^2=4`

Refine 4:

`(x+2)^2+y^2=4`

Rewrite in standard form:

`(x-(-2))^2+(y-0)^2=2^2`

Therefore the circle properties are:

center: (a,b)=(-2,0) radius: r=2

Finally, drawing the graph of the equation: