$\"\"$

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(a)

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The circle equation is $\"x^2+y^2+x+y-\\frac{1}{2}=0\"$ .

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The standard form of circle is $\"\\left$ .

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Where center is $\"\\left$ and radius is $\"r\"$ .

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Convert the given circle equation into standardform.

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$\"x^2+x+y^2+y=\\frac{1}{2}\"$

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To complete the square add $\"(\"$ half the $\"x\"$ coefficient $\")^2\"$ and $\"(\"$ half the $\"y\"$ coefficient $\")^2\"$ to each side of equation.

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$\"(\"$ half the $\"x\"$ coefficient $\")^2\"$ $\"=\\left$ .

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$\"(\"$ half the $\"y\"$ coefficient $\")^2\"$ $\"=\\left$ .

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$\"x^2+x+\\frac{1}{4}+y^2+y+\\frac{1}{4}=\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{4}\"$

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$\"\\left$

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$\"\\left$

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Compare it with standardform $\"\\left$ .

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Center $\"\\left$ and radius $\"r=1\"$ .

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$\"\"$

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$\"\\left$

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Graph the circle with center $\"\\left$ and radius $\"r=1\"$ .

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Find four points " radius away from the center in the up, down , left and right direction"

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Up $\"\\left$ ,

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Down $\"\\left$ ,

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Left $\"\\left$ and

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Right $\"\\left$ .

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Graph :

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Draw the coordinate plane.

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Plot the center at $\"\\left$ .

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Plot four points " radius away from the center in the up, down , left and right direction".

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Sketch the circle.

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$\"\"$

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$\"\"$

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$\"\\left$

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The circle equation is $\"x^2+y^2+x+y-\\frac{1}{2}=0\"$ .

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Find the intercepts.

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First find the $\"x\"$ intercept by substituting $\"y=0\"$ in the original equation.

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$\"\\\\x^2+0^2+x+0-\\frac{1}{2}=0\\\\x^2+x-\\frac{1}{2}=0\"$

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Compare with quadratic form $\"ax^2+bx+c=0\"$ .

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$\"a=1,$ .

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$\"x=\\frac{-b\\pm$

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$\"x=\\frac{-1\\pm$

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$\"x=\\frac{-1\\pm$

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$\"x=\\frac{-1\\pm$

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$\"x=\\frac{-1+$ and $\"x=\\frac{-1-$ .

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$\"x\"$ -intercepts are $\"\\frac{-1+$ and $\"\\frac{-1-$ .

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Next find the $\"y\"$ intercept by substituting $\"x=0\"$ in the original equation.

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$\"0^2+y^2+0+y-\\frac{1}{2}=0\"$

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$\"y^2+y-\\frac{1}{2}=0\"$

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Solve the equation by using quadratic formula.

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$\"y\"$ -intercepts are $\"\\frac{-1+$ and $\"\\frac{-1-$ .

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$\"\"$

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$\"\\left$ Center $\"\\left$ and radius $\"r=1\"$ .

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$\"\\left$ The circle graph :

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$\"\"$

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$\"\\left$

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$\"x\"$ -intercepts are $\"\\frac{-1+$ and $\"\\frac{-1-$ .

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$\"y\"$ -intercepts are $\"\\frac{-1+$ and $\"\\frac{-1-$ .