Pre-Calculus Prep: Graphing Parametric Equations x=t, y=t^2/4 (Parabola)

In pre-calculus, graphing parametric equations allows us to visualize curves and shapes by expressing the coordinates of points on the graph as functions of a third variable, usually denoted as 't'. Let's explore the parametric equations x = t and y = t^2/4, which represent a parabolic curve.

1. Identify the variables: In this case, we have the variables x and y, which represent the coordinates of points on the graph.

2. Plotting points: To graph the parabola, we need to substitute different values of 't' into the parametric equations and plot the corresponding (x, y) pairs on a coordinate plane. Choose a range of values for 't' that will give you a good representation of the shape of the curve.

3. Table of values: Create a table to organize the values of 't', 'x', and 'y'. For example:

| t | x | y |
|-------|-------|-------|
| -2 | -2 | 1 |
| -1 | -1 | 1/4 |
| 0 | 0 | 0 |
| 1 | 1 | 1/4 |
| 2 | 2 | 1 |

4. Plotting the points: Using the values from the table, plot the corresponding (x, y) pairs on the coordinate plane. Each point represents a specific value of 't' on the curve. Connect the points smoothly to obtain the shape of the parabolic curve.

5. Shape of the parabola: By connecting the points, you will observe that the graph forms a symmetrical parabolic shape that opens upwards or downwards. In this case, the vertex of the parabola is located at the point (0, 0), and the curve opens upward.

6. Optional: If desired, you can add additional points by selecting more values of 't' and calculating the corresponding (x, y) pairs. This will help in getting a clearer picture of the shape and any important features of the parabola.

Remember to label the axes, indicate any relevant coordinates or points on the graph, and use a suitable scale for your coordinate plane.

By following these steps and plotting the points obtained from the parametric equations x = t and y = t^2/4, you can graph a parabolic curve in pre-calculus.
These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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