A coordinate plane is a two-dimensional surface formed by the intersection of a vertical line (y-axis) and a horizontal line (x-axis). These axes divide the plane into four quadrants used for graphing equations and geometric shapes.
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The origin of the coordinate plane is at (0,0), where the x-axis and y-axis intersect.
In the context of parabolas, their vertex can be located anywhere on the coordinate plane.
A parabola's orientation (opening up or down) can be determined by its equation in standard form $y = ax^2 + bx + c$ or vertex form $y = a(x-h)^2 + k$.
The focus and directrix of a parabola are also plotted on the coordinate plane, influencing its shape and direction.
Symmetry in parabolas can be analyzed using the axis of symmetry, which is a vertical line passing through the vertex.