Graph each pair of parametric equations. (2 points each) x = 3 sin^3t y = 3 cos^3t
1 answer:
A graphing calculator or graphing software is required to plot these functions.
Graphing the functions manually requires creating a table as shown below.
For the sake of brevity, only a few points are shown in the table.
For the plot shown below, the spacing in t/π is 0.05 instead of 0.5.
t/π x(t) y(t)
------ ----------- -----------
0 0 1
0.5 0.0040 0.9626
1.0 0.0307 0.8567
1.5 0.0970 0.7006
2.0 0.2101 0.5199
2.5 0.3646 0.3426
3.0 0.5439 0.1928
3.5 0.7230 0.0858
4.0 0.8739 0.0252
Graphing the functions manually requires creating a table as shown below.
For the sake of brevity, only a few points are shown in the table.
For the plot shown below, the spacing in t/π is 0.05 instead of 0.5.
t/π x(t) y(t)
------ ----------- -----------
0 0 1
0.5 0.0040 0.9626
1.0 0.0307 0.8567
1.5 0.0970 0.7006
2.0 0.2101 0.5199
2.5 0.3646 0.3426
3.0 0.5439 0.1928
3.5 0.7230 0.0858
4.0 0.8739 0.0252
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Answer:
Step-by-step explanation:
Given:
The function,
A standard parabola with vertex at origin is represented as:
The above function is a standard parabola with vertex at origin and opening upward.
The vertex of the above function is at the origin and the value of
is 1.
Now, the function is translated 4 units up.
So, from the rule of function transformations, if a graph is moved up by units, then
units is added to the function.
Therefore,
.
Also, the vertex of will be translated 4 units up. So, the co-ordinates of the vertex of
will be
Now, express the above function in the vertex form .
We have
This gives,