8. Conic Sections

Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. x² + 6x - 4y + 1 = 0

Identify each equation without completing the square. y² - 4x + 2y + 21 = 0

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? y² + 6y - x + 5 = 0

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function?

$y=-x^2+4x-3$

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\{\begin{array}{c}{(y-2)}^2=x+4\\ y=-\text{(}\frac{1}{2}\text{)}x\end{array}$

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\{\begin{array}{c}x=y^2-3\\ x=y^2-3y\end{array}$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $\begin{cases}x = (y + 2)^2 - 1 \\(x - 2)^2 + (y + 2)^2 = 1\end{cases}$

In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). y^2 = - 4x