Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.

[x^2 − 4x + y^2 + 8y = −4]

x² − 4x + y² + 8y = −4

x^2 - 4x + (4/2)²  +    y² + 8y + (8/2)²  =  -4 + (4/2)²  +(8/2)²

(x - 2)² + (y + 4)² = -4 + 4 + 16 = 16

(x - 2)² + (y + 4)²  = 4²

That's a circle with

center (2,-4)  radius 4

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: