Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?
Rewrite the function
f(x)=x^2+13/3 x+7/3
in the form
f(x)=(x+13/6)^2+ c
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.
https://brainmass.com/math/graphs-and-functions/finding-vertex-intercepts-repel-attract-4561
Solution Preview
f(x)=x^2+13/3x+7/3
=x^2+2*(13/6)x+(13/6)^2-(13/6)^2+7/3
=(x+13/6)^2-169/36+7/3
=(x+13/6)^2-169/36+84/36
=(x+13/6)^2-85/36
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).
Y-intercept:
Let x=0 then ...
Solution Summary
The vertex and intercepts of a parabola are located. The repulsion, attaction and indifference are examined.