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1. Completing the square parameter ●○○○○ 10 ptsThe equation $x^2 + 2x - 2 = 0$ is transformed into the form $(x + m)^2 = 3$ by completing the square. Find the value of $m$.
2. Center of a circle from general form ●○○○○ 10 ptsFind the coordinates of the center of the circle $x^2 + y^2 - 4x + 2y - 1 = 0$. Give the $x$-coordinate and the $y$-coordinate.
3. Centre of a circle from its equation ●○○○○ 10 ptsFind the coordinates $(a, b)$ of the centre of the circle $x^2+y^2+6x-8y-24=0$.
4. Area enclosed by a parametric curve ●●○○○ 20 ptsFind the area of the region enclosed by the parametric curve $x = 6\cos^2 t$, $y = 6\cos t\sin t$. Round to two decimal places.
5. Quadratic expression in shifted variables ●●○○○ 20 ptsGiven $a=2009x+2007$, $b=2009x+2008$, $c=2009x+2009$, find the value of $a^{2}+b^{2}+c^{2}-ab-bc-ca$.
6. Completing the square for a quartic ●●○○○ 20 ptsRewrite the expression $g^4 + 12g^2 + 9$ in the form $c(g^2 + p)^2 + q$. What is $q$?
7. Roots by completing the square ●●○○○ 20 ptsFind the roots of $2x^2 - 7x + 3 = 0$ by completing the square.