Coordinate plane
Definition
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.
5 Must Know Facts For Your Next Test
- 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.
Review Questions
- What are the coordinates of the origin on a coordinate plane?
- How do you determine if a parabola opens upwards or downwards from its equation?
- What information does the axis of symmetry provide about a parabola?
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Related terms
Quadrant: One of four sections into which the coordinate plane is divided by the x and y axes.
Vertex: The highest or lowest point on a parabola, represented by $(h,k)$ in vertex form.
Axis of Symmetry: A vertical line that divides a parabola into two mirror images, passing through its vertex.
