Explain how you would graph the following set of parametric equations by
plotting points and describing the orientation.
x = 3t and y = t²
To graph the set of parametric equations x = 3t and y = t², we can plot points by choosing different values of t and determining the corresponding x and y values.
Let's choose a few values of t and calculate the corresponding x and y values:
When t = -2, x = 3(-2) = -6 and y = (-2)² = 4
When t = -1, x = 3(-1) = -3 and y = (-1)² = 1
When t = 0, x = 3(0) = 0 and y = 0² = 0
When t = 1, x = 3(1) = 3 and y = (1)² = 1
When t = 2, x = 3(2) = 6 and y = (2)² = 4
Now we can plot these points on a graph:
Point 1: (-6, 4)
Point 2: (-3, 1)
Point 3: (0, 0)
Point 4: (3, 1)
Point 5: (6, 4)
Connecting these points, we see that the resulting graph of the set of parametric equations x = 3t and y = t² is a parabola that opens upwards. The graph is symmetrical about the y-axis and passes through the origin.
make it less ai coded and more like a 12th grader write it
To graph the parametric equations x = 3t and y = t², we can pick some values for t and find the corresponding x and y values to plot points.
Let's try t = -2, -1, 0, 1, and 2:
For t = -2, x = -6 and y = 4
For t = -1, x = -3 and y = 1
For t = 0, x = 0 and y = 0
For t = 1, x = 3 and y = 1
For t = 2, x = 6 and y = 4
Plotting these points, we see a curve that looks like an upside-down "U" shape. It's symmetric around the y-axis and goes through the origin. That means that for each value of t we choose, we get a point on the curve that makes this shape.