Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?
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Rewrite the function
in the form
Then need to find the vertex of parabola as the graph of f, finding the y and x intercepts.
Find the fixed points of f state whether they repel, attract or are indifferent.
Using a gradient, find the interval of attraction for one of the fixed points.
Vertex: Notice that if we take x^2, shift it to the left by 13/6
and then shift it down by 85/36, we get f(x). Vertex of x^2
is (0,0), so the vertex of this parabola is (-13/6,-85/36).
Let x=0 then ...
The vertex and intercepts of a parabola are located. The repulsion, attaction and indifference are examined.