Graphing (x - 3)² + (y + 2)² = 25

Algebra 2 · Axiom Academy

EXAMPLE Graphing (x-3)^2+(y+2)^2=25 Identify a circle's center and radius from standard form, then plot it point by point. Identify the center and radius of the circle (x-3)^2+(y+2)^2=25 , then graph it on the coordinate plane. Center (3,-2) , radius 5 — plotted with the four key points and the completed circle. Nice work — you graphed a circle straight from its equation. The pieces worth keeping: Standard form: (x-h)^2+(y-k)^2=r^2 , where (h,k) is the center and r is the radius. Watch the signs: (x-3) gives h=+3 , while (y+2) gives k=-2 (rewrite it as y-(-2) first). Find the radius: take the square root of the constant on the right side — . Plot strategically: start at the center, then move r units in each of the four cardinal directions. Connect smoothly: a circle is exactly the set of points a fixed distance r from the center. This method works for any circle in standard form — find the center, find the radius, plot four points, and connect them.

This is the written version of the interactive lesson above. See the full Algebra 2 course.