A circle with equation \(x^2+y^2=144\) is graphed in the standard \((x,y)\) coordinate plane. At what points does the circle intersect the \(x\)-axis?

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The equation of a circle:

$$ (x-h)^2+(y-k)^2=r^2 $$

This circle has a center at \((0,0)\) and a radius of 12. We can go 12 to the left and to the right to get the \(x\)-intercepts.

$$ x^2+y^2=144 $$ $$ x^2 +(0)^2=144 $$ $$ x^2 = 144 $$ $$ x =\pm \sqrt{144} $$ $$ x=\pm 12 $$