PRECALCULUS

• A parabola is the set of all points in the plane equidistant from a fixed point called the focus and a fixed line called the directrix
• Focus: the fixed point in a parabola
• Directrix: the fixed line in a parabola
• The parabola is composed of points having the same distance from the focus and the directrix
• Vertex: the midpoint between the focus and the directrix
• Axis of symmetry: the line passing through the focus and the vertex, dividing the parabola into two congruent regions
• Focal length: the distance between the vertex and the focus, denoted as c
• Latus rectum: the line segment passing through the focus, perpendicular to the axis of symmetry, with a length denoted as 4c
• The parabola can open to the left and to the right, not just upward or downward
• Standard equation for a parabola opening upward or downward: x - h squared = 4c(y - k)
• Standard equation for a parabola opening to the right or left: y - k squared = 4c(x - h)
• The variable that is squared in the equation determines the direction in which the parabola opens: x for upward or downward, y for right or left