91Ó°ÊÓ

CONCEPTS Fill in the blanks. To complete the square on \(x^{2}+2 x\) and on \(y^{2}-6 y,\) what numbers must be added to each side of the equation? $$ \begin{aligned} x^{2}+2 x+y^{2}-6 y &=2 \\ x^{2}+2 x+&+y^{2}-6 y+\quad 2+ \end{aligned} $$

CONCEPTS A. What is the standard form of the equation of a parabola opening upward or downward? B. What is the standard form of the equation of a parabola opening to the right or left?

CONCEPTS Determine whether the graph of each equation is a circle or a parabola. A. \(x^{2}+y^{2}-6 x+8 y-10=0\) B. \(y^{2}-2 x+3 y-9=0\) C. \(x^{2}+5 x-y=0\) D. \(x^{2}+12 x+y^{2}=0\)

Solve each system of equations by graphing. See Example 1. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=9 \\ y-x=3 \end{array}\right. $$

Graph each equation. See Example 1 . $$ \frac{x^{2}}{25}+\frac{y^{2}}{4}=1 $$

Write the equation of a circle in standard form with the following properties. Center at the origin; radius 1

Write the equation of a circle in standard form with the following properties. Center at \((-2,6) ;\) radius 12

Solve each system of equations by substitution for real values of x and y. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=20 \\ y=x^{2} \end{array}\right. $$

Graph each equation. See Example 4. $$ x y=4 $$

Write each equation of a parabola in standard form and graph it. Give the coordinates of the vertex. $$ y=-x^{2}-2 x+3 $$