The axis of symmetry is a line where if you were to fold the graph in half on that line, every point should perfectly match up with it's opposite.
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
All of the points on a parabola define a parabola. However, the vertex is the point in which the y value is only used for one point on the parabola.
Select a set of x values and find the value of y or f(x) - depending on how the parabola is defined. These are the values that you need to graph.
It depends on where points h and k are, in which parabola. Since you have chosen not to share that information, there cannot be any sensible answer to this question.
The set of all points in a plane that are equidistant from a single point and a single line
To graph a parabola you must find the axis of symmetry, determine the focal distance and write the focal as a point, and find the directrix. These are all the main points you need to be able to draw a parabola.
halfway points
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
Halfway Points
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
It is the midpoint
A parabola has one vertex (but not in the sense of an angle), infinitely many points and no edges.
Knoxville, Tennessee is about halfway between these two points.
The city halfway between those two points is Tolland, CT.
The halfway points are the points which mark the half distance covered by the flight. These lie in the mid of both the above mentioned places. These points change for different locations. Halfway points for the above mentioned places are Ghent, WV.
For example, y = ax2 + bx + c (the equation of a parabola). Every parabola has an axis of symmetry and the graph to either side of the axis of symmetry is a mirror image of the other side. It means that if we know a point on one side of the parabola, we can find its symmetric point to the other side, based on the axis of symmetry. Those symmetric points have opposite x-coordinate values, and the same y-coordinate value. The vertex only is a single point which lies on the axis of symmetry.
The halfway points are the points which mark the half distance covered by the flight. These lie in the mid of both the above mentioned places. These points change for different locations. Halfway points for the above mentioned places are - Northampton.