The following equation is that of a parabola. Using its vertex and the direction in which it opens, solve for its domain and range, and tell if the given relation is a function or not.

y = - x² + 10x - 21

Write the equation of the parabola in standard form given the following conditions.

Focus (6, 1), Directrix: x = - 4

Write the equation of the parabola in standard form given the following conditions.

Vertex: (1, - 4); Focus: (1, - 9)

By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.
y = x² +11
y = x² -11x

By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.
x² + 10x - 12y + 13 = 0