How do you graph the circle with center at (-4, 2) and radius 5 and label the center and at least four points on the circle, then write the equation of the circle?

By using the center-radius form. The center is ##C## at ##(h,k)## meaning ##h = -4## and ##k = 2##. The equation will be ##(x - h)^2 + (y - k)^2 = r^2## That translates to: ##(x + 4)^2 + (y - 2)^2 = 25## Expanding, we get ##x^2 + 8x + 16 + y^2 - 4y + 4 = 25## or ##x^2 + 8x + y^2 - 4y - 5 = 0##

For the graphing part, locate the center ##(-4,2)##. Open your compass 5 units to any direction, then make a circle. It should pass the following points (along with infinitely many other points): ##(-4 + 5, 2)## ##->## ##(1,2)## ##(-4 - 5,2)## ##->## ##(-9, 2)## ##(-4, 2 + 5)## ##->## ##(-4, 7)## ##(-4, 2 - 5)## ##->## ##(-4, -3)##