Example function.
Y = X2 - 4X + 5
set to 0
X2 - 4X + 5 = 0
X2 - 4X = - 5
Now, halve the linear coefficient, square it and add it to both sides
X2 - 4X + 4 = - 5 + 4
gather terms on the right and factor on the left
(X - 2)2 = -1
==============Vertex form.
(2, - 1)
=======Vertex.
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If the graph start and end with same vertex and no other vertex can be repeated then it is called trivial graph.
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
x2+8= y This equation represents a function. It will be a parabola with the vertex at (0,8). You can easily graph this on a graphing calculator or from prior knowledge. You know the basic graph of y=x2 with vertex (0,0) and opens upwards on the y-axis. From the equation, you simply shift the vertex vertically up 8 so the new vertex is (0,8) This represents a function because for every x value there is one y value.
range is the y values in a graph otherwise known as a function; for example in the graph y= abs(x), the graph is a v with the vertex at the origin and the range is (0,infinity).
A vertex of a graph is said to be pendant if its neighborhood contains exactly one vertex.