Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?
Not what you're looking for?
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.
Purchase this Solution
Solution Summary
The vertex and intercepts of a parabola are located. The repulsion, attaction and indifference are examined.
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 ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.