Welcome! Today we'll learn how to draw a parabola. A parabola is a U-shaped curve that follows a quadratic equation like y equals x squared. The most important point on a parabola is called the vertex, which is the lowest or highest point of the curve.
The first step in drawing a parabola is to create a table of values. We choose several x-values and calculate the corresponding y-values using our equation. For example, when x equals negative 2, y equals 4. When x equals negative 1, y equals 1. At the vertex where x equals 0, y equals 0. The pattern continues symmetrically on the positive side.
Now we plot these points on our coordinate axes and connect them with a smooth curve. It's important to draw a smooth, continuous curve rather than connecting the points with straight lines. Notice that the parabola is perfectly symmetric around the y-axis, which is called the axis of symmetry.
Parabolas can open in different directions depending on their equation. The standard parabola y equals x squared opens upward. If we change it to y equals negative x squared, it opens downward. We can also have parabolas that open sideways, like x equals y squared, which opens to the right.
To summarize what we've learned about drawing parabolas: First, create a table of values using your equation. Then plot these points on coordinate axes. Connect the points with a smooth curve, not straight lines. Remember that parabolas are symmetric and can open in different directions depending on the equation. The vertex is always the most important reference point.