Parabola
A parabola is a U-shaped curve that can open upward or downward
A parabola is a U-shaped curve that can open upward or downward. It is a type of conic section, which is formed by the intersection of a plane and a double-napped cone. The equation of a parabola can be written in the form:
y = a(x – h)^2 + k
In this equation, (h, k) represents the coordinates of the vertex, and ‘a’ determines the shape of the parabola. If ‘a’ is positive, the parabola opens upward, and if ‘a’ is negative, it opens downward.
The vertex of a parabola is an important point because it represents the minimum or maximum point depending on the direction of opening. The axis of symmetry of the parabola is a vertical line passing through the vertex. It divides the parabola into two equal halves.
To graph a parabola, you can follow these steps:
1. Identify the vertex: The vertex is in the form (h, k), where h and k are the x and y coordinates of the vertex. If the equation of the parabola is not in the standard form, you may need to convert it first.
2. Find the axis of symmetry: The axis of symmetry is a vertical line passing through the vertex. Its equation is x = h.
3. Determine the direction of the parabola: Look at the coefficient ‘a’ in the equation. If ‘a’ is positive, the parabola opens upward, and if ‘a’ is negative, it opens downward.
4. Find additional points: Choose a few more x values on both sides of the axis of symmetry, plug them into the equation, and solve for the corresponding y values to get additional points on the parabola.
5. Plot the points and draw the curve: Plot the vertex, the additional points, and any other key points you may have (e.g., y-intercept). Connect the points with a smooth U-shaped curve.
Remember that the specific shape and position of a parabola may vary depending on the values of ‘a’, ‘h’, and ‘k’ in the equation. However, these general steps can help you graph any parabola.
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