Parametric cubic equation
General Contents
Detailed Contents
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Solve and graph
.
First determine some points on the
x-y
graph, using the “
t
” values -2, -1, 0, 1, 2.
We get
t
-2
-1
0
1
2
x
-4
-3
-2
-1
0
y
-8
-1
0
1
8
Try to plot this graph without using your graphing calculator. Then check.
alt="Graph of a cubic. Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!
What typical curve does this look like?
A cubic.
Is it centered on the origin like
?
No.
Where is it centered?
At
x
= – 2.
Let’s determine the rectangular equation of this curve. How do we do that?
Since one equation is linear in “
t
”, solve that one for
t
.
From the “
x
”equation, we get
Substitute this result into the “
y
” equation.
We get
.
Compare this to the graph.
This equation is of the form
, where
h
= -2.
What is the meaning of
h
here?
h
is the
x
-coordinate of the “center” of the cubic, and matches our graph.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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General Contents
Detailed Contents
Index