Chapter 13

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

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=3 y^{2} $$

Graph each inequality. $$ y

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{r} x^{2}+y^{2}=25 \\ 4 x+3 y=0 \end{array}\right. $$

Graph each ellipse. $$ \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 $$

Graph each inequality. $$ y<-x^{2} $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{r} x^{2}+y^{2}=25 \\ 3 x+4 y=0 \end{array}\right. $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=5 y^{2} $$

Graph each ellipse. $$ \frac{x^{2}}{9}+y^{2}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=-2 y^{2} $$

Graph each inequality. $$ x^{2}+y^{2} \geq 16 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{aligned} x^{2}+4 y^{2} &=10 \\ y &=x \end{aligned}\right. $$

Graph each ellipse. $$ x^{2}+\frac{y^{2}}{4}=1 $$

Graph each inequality. $$ x^{2}+y^{2}<36 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{aligned} 4 x^{2}+y^{2} &=10 \\ y &=x \end{aligned}\right. $$

Graph each ellipse. $$ 9 x^{2}+4 y^{2}=36 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=-4 x^{2} $$

Graph each inequality. $$ \frac{x^{2}}{4}-y^{2}<1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y^{2}=4-x \\ x-2 y=4 \end{array}\right. $$

Graph each ellipse. $$ x^{2}+4 y^{2}=16 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=-2 x^{2} $$

Graph each inequality. $$ x^{2}-\frac{y^{2}}{9} \geq 1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=4 \\ x+y=-2 \end{array}\right. $$

Graph each ellipse. $$ 4 x^{2}+25 y^{2}=100 $$

Graph each inequality. $$ y>(x-1)^{2}-3 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{aligned} x^{2}+y^{2} &=9 \\ 16 x^{2}-4 y^{2} &=64 \end{aligned}\right. $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=(y-2)^{2}+3 $$

Graph each ellipse. $$ 36 x^{2}+y^{2}=36 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=(y-4)^{2}-1 $$

Graph each inequality. $$ y>(x+3)^{2}+2 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} 4 x^{2}+3 y^{2}=35 \\ 5 x^{2}+2 y^{2}=42 \end{array}\right. $$

Graph each ellipse. $$ \frac{(x+1)^{2}}{36}+\frac{(y-2)^{2}}{49}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=-3(x-1)^{2}+5 $$

Graph each inequality. $$ x^{2}+y^{2} \leq 9 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+2 y^{2}=2 \\ x-y=2 \end{array}\right. $$

Graph each ellipse. $$ \frac{(x-3)^{2}}{9}+\frac{(y+3)^{2}}{16}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=-4(x-2)^{2}+2 $$

Graph each inequality. $$ x^{2}+y^{2}>4 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+2 y^{2}=2 \\ x^{2}-2 y^{2}=6 \end{array}\right. $$

Graph each ellipse. $$ \frac{(x-1)^{2}}{4}+\frac{(y-1)^{2}}{25}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ x=y^{2}+6 y+8 $$

Graph each inequality. $$ y>-x^{2}+5 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=x^{2}-3 \\ 4 x-y=6 \end{array}\right. $$

Graph each ellipse. $$ \frac{(x+3)^{2}}{16}+\frac{(y+2)^{2}}{4}=1 $$

Graph each inequality. $$ y<-x^{2}+5 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=x+1 \\ x^{2}-y^{2}=1 \end{array}\right. $$

Graph each hyperbola. $$ \frac{x^{2}}{4}-\frac{y^{2}}{9}=1 $$

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. See Examples 1 through 4. $$ y=x^{2}+10 x+20 $$

Graph each inequality. $$ \frac{x^{2}}{4}+\frac{y^{2}}{9} \leq 1 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{aligned} y &=x^{2} \\ 3 x+y &=10 \end{aligned}\right. $$