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# Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?

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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.

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