3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
Learning Goals
1.
To be able to graph the reciprocal of a quadratic
function by considering its end behaviours as well as its
behaviour around its asymptotes.
2. To be able to discuss the change in slope of the
function.
3.2 - Reciprocal of a Quadratic Function
Reciprocals of quadratic functions with two zeros have
three parts, with the middle one reaching a maximum or
minimum point. This point is equidistant from the two
vertical asymptotes.
For example, the reciprocal of a quadratic function may
look like the following:
This is a negative quadratic
reciprocal function.
This is a positive quadratic reciprocal
function.
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
Steps For Graphing the Reciprocal of a Quadratic Function
1.
Solve for the vertical asymptotes. You may have to factor
first.
2.
Describe the behaviour of the function on either side of the
asymptotes.
3.
Describe the end behaviours.
4.
Calculate the max or min co-ordinate (solve for A.O.S. and plug
into function to solve for y).
5.
Sketch the graph.
Example One
Consider the function
a) State the domain.
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
b) Find the equations of the asymptotes.
c) Describe the behaviour of the function near the
asymptotes.
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
d) Describe the end behaviours.
e) Determine the x- and y-intercepts.
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
f) Sketch a graph of the function.
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
g) State the range.
Intervals will always be based on the vertical
asymptotes AND the location of the axis of
symmetry (A.O.S.).
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
Example Two
a) Describe the increasing and decreasing intervals in the
branches of the function
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3.2 Reciprocal of a Quadratic Function.notebook
March 12, 2015
Complete: p. 164 - 167 # 1,2,5ab,8ad,11a.
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